Physics Book - User contributions [en]

Speed of Sound in Solids

2015-12-06T00:49:33Z

Dpatel322: /* References */

This page discusses calculating the speed of sound in various solids and provides examples of such calculations.

==The Main Idea==

The speed of sound is the speed that sound wave travels through a particular medium. In comparison to air, sound travels considerably faster in solids. The speed that sound travels in various solids depends on the solid's density and elasticity, as these factors effect the ability of the sound waves vibrational energy to transfer across the solid medium.

===A Mathematical Model===

The speed of sound in solids <math> {V_{s}} </math> can be determined by the equation. Young's Modulus is a measure of elasticity of an object, and it can be computed to solve for interatomic values, such as interatomic bond stiffness or interatomic bond length.

<math> {V_{s}} = d* √ (K_{s}/m_{atom}) </math>

<math> d </math> = interatomic bond length

<math> K_{s} </math> = Interatomic bond stiffness

Youngs Modulus = (<math> Y = K_{s}/d </math>)

Youngs Modulus: <math> Y ={\frac{Stress}{Strain}}</math>

<math> Stress = {\frac{F_{tension}}{Area_{Cross Sectional}}} </math>

<math> Strain = {\frac{ΔL_{wire}}{L_{0}}} </math>

===Speeds of Various Compositions===
[[File:speedofsound.jpg]]

==Examples==

Be sure to show all steps in your solution and include diagrams whenever possible

===Theoretical===

Two metal rods are made of different elements. The interatomic spring stiffness of element A is four times larger than the interatomic spring stiffness for element B. The mass of an atom of element A is four times greater than the mass of an atom of element B. The atomic diameters are approximately the same for A and B. What is the ratio of the speed of sound in rod A to the speed of sound in rod B?

Solution: In this situation, the ratio of the speed of sound in rod A to the speed of sound in rod B is 1.

Looking at the formula for computing speed of sound in solids, <math> {V_{s}} = d* √ (K_{s}/m_{atom}) </math>, you see that velocity depends three factors, interatomic stiffness, the mass of one atom, and interatomic bond length. The two rods differences in atomic mass and interatomic stiffness offset each other when the equations are set equal, and the ratio is determined to be 1.

<math> d* √ 4(K_{s}/m_{atom}) = d* √ (K_{s}/4m_{atom}) </math> After simplification <math> V_{s_{1}} = V_{s{2}} </math>

===Numerical Example ===
The Young's Modulus value of silver is 7.75e+10, atomic mass of silver is 108 g/mole, and the density of silver is 10.5 g/cm3. Using this information, calculate the speed of sound in silver.

Solution: The key to solving this problem is to realize the micro-macro connection of Young's Modulus. You are given that Young's Modulus is equal to 7.75e+10, and we know that
Youngs Modulus = (<math> K_{s}/d </math>). In this situation, we need to calculate the interatomic bond length and use it and our Young's Modulus value to determine our interatomic stiffness.

To solve for ''d'', we use the given density of silver (10.5 g/cm3). Using the basic equation for volume in relation to density and mass (<math> V=m*d</math>), we can find ''d'', since ''d'' is equal to the cube root of volume.

Once ''d'' is solved for, it can be plugged back into the the equation <math> Y = K_{s}/d </math> to solve for <math> K_{s} </math>

Now, we have solved for both interatomic bond length and stiffness. The only quantity in the final speed of sound equation we need is the mass of one atom, which can be determined using Avogardro's number and the atomic mass. <math> m_{atom} = </math> ''atomic mass'' / <math> 6.022e23 </math>

Now that all variables are solved for, we can substitute values into our <math> {V_{s}} = d* √ (K_{s}/m_{atom}) </math> equation.

<math> {V_{s}} = 1.6e-10* √ (78534.7/1.79e-22) </math>

<math> {V_{s}} = 2723</math> m/s

==Connectedness==
The computation of speed of sound in solids is dependent on a mass' interatomic properties, such as interatomic bond length. I find it interesting when a object's interatomic properties determine its functionality on a larger scale. In the case of speed of sound in solids, the objects elasticity depends on the interatomic bond length.

While the computation of speed of sound in solids may not seem related to Industrial Engineering, it has clear implications in the process of choosing building materials, which is a notable section of industrial engineering. For example, if you are planning to build something soundproof, it would be optimal to choose a solid with a very low speed of sound velocity.

The industrial applications in terms of construction are vast. An objects ability to block/allow sound waves through it is very important. Of course, insulation materials and sound proof wall materials come to thought at first. However, in some cases, contractors need to build structures that allow sound to travel through, in which they would choose solid materials that correlate with high speeds of sound.

==History==

The speed of sound in air was first measured by Sir Isaac Newton, and first correctly computed by Pierre-Simon Laplace in 1816. Before this precise measurement, attempts had been made across Europe during the 1700s, most famously Reverend William Derham's experiment in 1709 across the town of Upminister, England. Reverend Derham used a shotgun's noise and several known landmarks around time to measure the time it took for the sound of the blast to be heard from select distances.

Young's Modulus was named after English physicist Thomas Young. In actuality, the concept was developed earlier by physicists Leonhard Euler and Giordano Riccati in the 1720s.

== See also ==

Youngs Modulus: [http://www.physicsbook.gatech.edu/Young%27s_Modulus]
Interatomic Bonds: [http://www.physicsbook.gatech.edu/Length_and_Stiffness_of_an_Interatomic_Bond]

===Further reading===

Further Information can be found on the speed of sound in solids in ''Matter and Interactions, 4th Edition'' by Ruth W. Chabay & Bruce A. Sherwood
===External links===

Internet resources on this topic can be found at:

Engineering Tool Box [http://www.engineeringtoolbox.com/sound-speed-solids-d_713.html]

Hyperphysics [http://hyperphysics.phy-astr.gsu.edu/hbase/sound/souspe2.html]

Potto Project [http://www.potto.org/gasDynamics/node73.html]

NDT Resource Center [https://www.nde-ed.org/EducationResources/CommunityCollege/Ultrasonics/Physics/elasticsolids.htm]

==References==

This section contains the the references used while writing this page

Chart from [http://www.rcgroups.com/forums/attachment.php?attachmentid=3397792]

''Matter and Interactions 4th Edition'' by Chabay and Sherwood

Wikipage created by Daiven Patel

Speed of Sound in Solids

2015-12-06T00:49:18Z

Dpatel322:

Speed of Sound in Solids

2015-12-06T00:42:10Z

Dpatel322: /* Numerical Example */

This page discusses calculating the speed of sound in various solids and provides examples of such calculations.
Claimed by Dpatel322 @ 12/1

==The Main Idea==

The speed of sound is the speed that sound wave travels through a particular medium. In comparison to air, sound travels considerably faster in solids. The speed that sound travels in various solids depends on the solid's density and elasticity, as these factors effect the ability of the sound waves vibrational energy to transfer across the solid medium.

===A Mathematical Model===

The speed of sound in solids <math> {V_{s}} </math> can be determined by the equation. Young's Modulus is a measure of elasticity of an object, and it can be computed to solve for interatomic values, such as interatomic bond stiffness or interatomic bond length.

<math> {V_{s}} = d* √ (K_{s}/m_{atom}) </math>

<math> d </math> = interatomic bond length

<math> K_{s} </math> = Interatomic bond stiffness

Youngs Modulus = (<math> Y = K_{s}/d </math>)

Youngs Modulus: <math> Y ={\frac{Stress}{Strain}}</math>

<math> Stress = {\frac{F_{tension}}{Area_{Cross Sectional}}} </math>

<math> Strain = {\frac{ΔL_{wire}}{L_{0}}} </math>

===Speeds of Various Compositions===
[[File:speedofsound.jpg]]

==Examples==

Be sure to show all steps in your solution and include diagrams whenever possible

===Theoretical===

Two metal rods are made of different elements. The interatomic spring stiffness of element A is four times larger than the interatomic spring stiffness for element B. The mass of an atom of element A is four times greater than the mass of an atom of element B. The atomic diameters are approximately the same for A and B. What is the ratio of the speed of sound in rod A to the speed of sound in rod B?

Solution: In this situation, the ratio of the speed of sound in rod A to the speed of sound in rod B is 1.

Looking at the formula for computing speed of sound in solids, <math> {V_{s}} = d* √ (K_{s}/m_{atom}) </math>, you see that velocity depends three factors, interatomic stiffness, the mass of one atom, and interatomic bond length. The two rods differences in atomic mass and interatomic stiffness offset each other when the equations are set equal, and the ratio is determined to be 1.

<math> d* √ 4(K_{s}/m_{atom}) = d* √ (K_{s}/4m_{atom}) </math> After simplification <math> V_{s_{1}} = V_{s{2}} </math>

===Numerical Example ===
The Young's Modulus value of silver is 7.75e+10, atomic mass of silver is 108 g/mole, and the density of silver is 10.5 g/cm3. Using this information, calculate the speed of sound in silver.

Solution: The key to solving this problem is to realize the micro-macro connection of Young's Modulus. You are given that Young's Modulus is equal to 7.75e+10, and we know that
Youngs Modulus = (<math> K_{s}/d </math>). In this situation, we need to calculate the interatomic bond length and use it and our Young's Modulus value to determine our interatomic stiffness.

To solve for ''d'', we use the given density of silver (10.5 g/cm3). Using the basic equation for volume in relation to density and mass (<math> V=m*d</math>), we can find ''d'', since ''d'' is equal to the cube root of volume.

Once ''d'' is solved for, it can be plugged back into the the equation <math> Y = K_{s}/d </math> to solve for <math> K_{s} </math>

Now, we have solved for both interatomic bond length and stiffness. The only quantity in the final speed of sound equation we need is the mass of one atom, which can be determined using Avogardro's number and the atomic mass. <math> m_{atom} = </math> ''atomic mass'' / <math> 6.022e23 </math>

Now that all variables are solved for, we can substitute values into our <math> {V_{s}} = d* √ (K_{s}/m_{atom}) </math> equation.

<math> {V_{s}} = 1.6e-10* √ (78534.7/1.79e-22) </math>

<math> {V_{s}} = 2723</math> m/s

==Connectedness==
The computation of speed of sound in solids is dependent on a mass' interatomic properties, such as interatomic bond length. I find it interesting when a object's interatomic properties determine its functionality on a larger scale. In the case of speed of sound in solids, the objects elasticity depends on the interatomic bond length.

While the computation of speed of sound in solids may not seem related to Industrial Engineering, it has clear implications in the process of choosing building materials, which is a notable section of industrial engineering. For example, if you are planning to build something soundproof, it would be optimal to choose a solid with a very low speed of sound velocity.

The industrial applications in terms of construction are vast. An objects ability to block/allow sound waves through it is very important. Of course, insulation materials and sound proof wall materials come to thought at first. However, in some cases, contractors need to build structures that allow sound to travel through, in which they would choose solid materials that correlate with high speeds of sound.

==History==

The speed of sound in air was first measured by Sir Isaac Newton, and first correctly computed by Pierre-Simon Laplace in 1816. Before this precise measurement, attempts had been made across Europe during the 1700s, most famously Reverend William Derham's experiment in 1709 across the town of Upminister, England. Reverend Derham used a shotgun's noise and several known landmarks around time to measure the time it took for the sound of the blast to be heard from select distances.

Young's Modulus was named after English physicist Thomas Young. In actuality, the concept was developed earlier by physicists Leonhard Euler and Giordano Riccati in the 1720s.

== See also ==

Youngs Modulus: [http://www.physicsbook.gatech.edu/Young%27s_Modulus]
Interatomic Bonds: [http://www.physicsbook.gatech.edu/Length_and_Stiffness_of_an_Interatomic_Bond]

===Further reading===

Further Information can be found on the speed of sound in solids in ''Matter and Interactions, 4th Edition'' by Ruth W. Chabay & Bruce A. Sherwood
===External links===

Internet resources on this topic can be found at:

Engineering Tool Box [http://www.engineeringtoolbox.com/sound-speed-solids-d_713.html]

Hyperphysics [http://hyperphysics.phy-astr.gsu.edu/hbase/sound/souspe2.html]

Potto Project [http://www.potto.org/gasDynamics/node73.html]

NDT Resource Center [https://www.nde-ed.org/EducationResources/CommunityCollege/Ultrasonics/Physics/elasticsolids.htm]

==References==

This section contains the the references used while writing this page

Chart from [http://www.rcgroups.com/forums/attachment.php?attachmentid=3397792]

''Matter and Interactions 4th Edition'' by Chabay and Sherwood

[[Category:Which Category did you place this in?]]

Speed of Sound in Solids

2015-12-06T00:41:21Z

Dpatel322:

This page discusses calculating the speed of sound in various solids and provides examples of such calculations.
Claimed by Dpatel322 @ 12/1

==The Main Idea==

The speed of sound is the speed that sound wave travels through a particular medium. In comparison to air, sound travels considerably faster in solids. The speed that sound travels in various solids depends on the solid's density and elasticity, as these factors effect the ability of the sound waves vibrational energy to transfer across the solid medium.

===A Mathematical Model===

The speed of sound in solids <math> {V_{s}} </math> can be determined by the equation. Young's Modulus is a measure of elasticity of an object, and it can be computed to solve for interatomic values, such as interatomic bond stiffness or interatomic bond length.

<math> {V_{s}} = d* √ (K_{s}/m_{atom}) </math>

<math> d </math> = interatomic bond length

<math> K_{s} </math> = Interatomic bond stiffness

Youngs Modulus = (<math> Y = K_{s}/d </math>)

Youngs Modulus: <math> Y ={\frac{Stress}{Strain}}</math>

<math> Stress = {\frac{F_{tension}}{Area_{Cross Sectional}}} </math>

<math> Strain = {\frac{ΔL_{wire}}{L_{0}}} </math>

===Speeds of Various Compositions===
[[File:speedofsound.jpg]]

==Examples==

Be sure to show all steps in your solution and include diagrams whenever possible

===Theoretical===

Two metal rods are made of different elements. The interatomic spring stiffness of element A is four times larger than the interatomic spring stiffness for element B. The mass of an atom of element A is four times greater than the mass of an atom of element B. The atomic diameters are approximately the same for A and B. What is the ratio of the speed of sound in rod A to the speed of sound in rod B?

Solution: In this situation, the ratio of the speed of sound in rod A to the speed of sound in rod B is 1.

Looking at the formula for computing speed of sound in solids, <math> {V_{s}} = d* √ (K_{s}/m_{atom}) </math>, you see that velocity depends three factors, interatomic stiffness, the mass of one atom, and interatomic bond length. The two rods differences in atomic mass and interatomic stiffness offset each other when the equations are set equal, and the ratio is determined to be 1.

<math> d* √ 4(K_{s}/m_{atom}) = d* √ (K_{s}/4m_{atom}) </math> After simplification <math> V_{s_{1}} = V_{s{2}} </math>

===Numerical Example ===
The Young's Modulus value of silver is 7.75e+10, atomic mass of silver is 108 g/mole, and the density of silver is 10.5 g/cm3. Using this information, calculate the speed of sound in silver.

Solution: The key to solving this problem is to realize the micro-macro connection of Young's Modulus. You are given that Young's Modulus is equal to 7.75e+10, and we know that
Youngs Modulus = (<math> K_{s}/d </math>). In this situation, we need to calculate the interatomic bond length and use it and our Young's Modulus value to determine our interatomic stiffness.

To solve for ''d'', we use the given density of silver (10.5 g/cm3). Using the basic equation for volume in relation to density and mass (<math> V=m*d</math>), we can find ''d'', since ''d'' is equal to the cube root of volume.

Once ''d'' is solved for, it can be plugged back into the the equation <math> Y = K_{s}/d </math> to solve for <math> K_{s} </math>

Now, we have solved for both interatomic bond length and stiffness. The only quantity in the final speed of sound equation we need is the mass of one atom, which can be determined using Avogardro's number and the atomic mass. <math> m_{atom} = </math> ''atomic mass'' / <math> 6.022e23 </math>

Now that all variables are solved for, we can substitute values into our <math> {V_{s}} = d* √ (K_{s}/m_{atom}) </math> equation.

<math> {V_{s}} = 1.6e-10* √ (78534.7/1.79e-22) </math>

<math> {V_{s}} = 2723 m/s </math>

==Connectedness==
The computation of speed of sound in solids is dependent on a mass' interatomic properties, such as interatomic bond length. I find it interesting when a object's interatomic properties determine its functionality on a larger scale. In the case of speed of sound in solids, the objects elasticity depends on the interatomic bond length.

While the computation of speed of sound in solids may not seem related to Industrial Engineering, it has clear implications in the process of choosing building materials, which is a notable section of industrial engineering. For example, if you are planning to build something soundproof, it would be optimal to choose a solid with a very low speed of sound velocity.

The industrial applications in terms of construction are vast. An objects ability to block/allow sound waves through it is very important. Of course, insulation materials and sound proof wall materials come to thought at first. However, in some cases, contractors need to build structures that allow sound to travel through, in which they would choose solid materials that correlate with high speeds of sound.

==History==

The speed of sound in air was first measured by Sir Isaac Newton, and first correctly computed by Pierre-Simon Laplace in 1816. Before this precise measurement, attempts had been made across Europe during the 1700s, most famously Reverend William Derham's experiment in 1709 across the town of Upminister, England. Reverend Derham used a shotgun's noise and several known landmarks around time to measure the time it took for the sound of the blast to be heard from select distances.

Young's Modulus was named after English physicist Thomas Young. In actuality, the concept was developed earlier by physicists Leonhard Euler and Giordano Riccati in the 1720s.

== See also ==

Youngs Modulus: [http://www.physicsbook.gatech.edu/Young%27s_Modulus]
Interatomic Bonds: [http://www.physicsbook.gatech.edu/Length_and_Stiffness_of_an_Interatomic_Bond]

===Further reading===

Further Information can be found on the speed of sound in solids in ''Matter and Interactions, 4th Edition'' by Ruth W. Chabay & Bruce A. Sherwood
===External links===

Internet resources on this topic can be found at:

Engineering Tool Box [http://www.engineeringtoolbox.com/sound-speed-solids-d_713.html]

Hyperphysics [http://hyperphysics.phy-astr.gsu.edu/hbase/sound/souspe2.html]

Potto Project [http://www.potto.org/gasDynamics/node73.html]

NDT Resource Center [https://www.nde-ed.org/EducationResources/CommunityCollege/Ultrasonics/Physics/elasticsolids.htm]

==References==

This section contains the the references used while writing this page

Chart from [http://www.rcgroups.com/forums/attachment.php?attachmentid=3397792]

''Matter and Interactions 4th Edition'' by Chabay and Sherwood

[[Category:Which Category did you place this in?]]

Speed of Sound in Solids

2015-12-06T00:38:02Z

Dpatel322: /* Numerical Example */

This page discusses calculating the speed of sound in various solids and provides examples of such calculations.
Claimed by Dpatel322 @ 12/1

==The Main Idea==

The speed of sound is the speed that sound wave travels through a particular medium. In comparison to air, sound travels considerably faster in solids. The speed that sound travels in various solids depends on the solid's density and elasticity, as these factors effect the ability of the sound waves vibrational energy to transfer across the solid medium.

===A Mathematical Model===

The speed of sound in solids <math> {V_{s}} </math> can be determined by the equation. Young's Modulus is a measure of elasticity of an object, and it can be computed to solve for interatomic values, such as interatomic bond stiffness or interatomic bond length.

<math> {V_{s}} = d* √ (K_{s}/m_{atom}) </math>

<math> d </math> = interatomic bond length

<math> K_{s} </math> = Interatomic bond stiffness

Youngs Modulus = (<math> Y = K_{s}/d </math>)

Youngs Modulus: <math> Y ={\frac{Stress}{Strain}}</math>

<math> Stress = {\frac{F_{tension}}{Area_{Cross Sectional}}} </math>

<math> Strain = {\frac{ΔL_{wire}}{L_{0}}} </math>

===Speeds of Various Compositions===
[[File:speedofsound.jpg]]

==Examples==

Be sure to show all steps in your solution and include diagrams whenever possible

===Theoretical===

Two metal rods are made of different elements. The interatomic spring stiffness of element A is four times larger than the interatomic spring stiffness for element B. The mass of an atom of element A is four times greater than the mass of an atom of element B. The atomic diameters are approximately the same for A and B. What is the ratio of the speed of sound in rod A to the speed of sound in rod B?

Solution: In this situation, the ratio of the speed of sound in rod A to the speed of sound in rod B is 1.

Looking at the formula for computing speed of sound in solids, <math> {V_{s}} = d* √ (K_{s}/m_{atom}) </math>, you see that velocity depends three factors, interatomic stiffness, the mass of one atom, and interatomic bond length. The two rods differences in atomic mass and interatomic stiffness offset each other when the equations are set equal, and the ratio is determined to be 1.

<math> d* √ 4(K_{s}/m_{atom}) = d* √ (K_{s}/4m_{atom}) </math> After simplification <math> V_{s_{1}} = V_{s{2}} </math>

===Numerical Example ===
The Young's Modulus value of silver is 7.75e+10, atomic mass of silver is 108 g/mole, and the density of silver is 10.5 g/cm3. Using this information, calculate the speed of sound in silver.

Solution: The key to solving this problem is to realize the micro-macro connection of Young's Modulus. You are given that Young's Modulus is equal to 7.75e+10, and we know that
Youngs Modulus = (<math> K_{s}/d </math>). In this situation, we need to calculate the interatomic bond length and use it and our Young's Modulus value to determine our interatomic stiffness.

To solve for ''d'', we use the given density of silver (10.5 g/cm3). Using the basic equation for volume in relation to density and mass (<math> V=m*d</math>), we can find ''d'', since ''d'' is equal to the cube root of volume.

Once ''d'' is solved for, it can be plugged back into the the equation <math> Y = K_{s}/d </math> to solve for <math> K_{s} </math>

Now, we have solved for both interatomic bond length and stiffness. The only quantity in the final speed of sound equation we need is the mass of one atom, which can be determined using Avogardro's number and the atomic mass. <math> m_{atom} = </math> ''atomic mass'' / <math> 6.022e23 </math>

Now that all variables are solved for, we can substitute values into our

==Connectedness==
The computation of speed of sound in solids is dependent on a mass' interatomic properties, such as interatomic bond length. I find it interesting when a object's interatomic properties determine its functionality on a larger scale. In the case of speed of sound in solids, the objects elasticity depends on the interatomic bond length.

While the computation of speed of sound in solids may not seem related to Industrial Engineering, it has clear implications in the process of choosing building materials, which is a notable section of industrial engineering. For example, if you are planning to build something soundproof, it would be optimal to choose a solid with a very low speed of sound velocity.

The industrial applications in terms of construction are vast. An objects ability to block/allow sound waves through it is very important. Of course, insulation materials and sound proof wall materials come to thought at first. However, in some cases, contractors need to build structures that allow sound to travel through, in which they would choose solid materials that correlate with high speeds of sound.

==History==

The speed of sound in air was first measured by Sir Isaac Newton, and first correctly computed by Pierre-Simon Laplace in 1816. Before this precise measurement, attempts had been made across Europe during the 1700s, most famously Reverend William Derham's experiment in 1709 across the town of Upminister, England. Reverend Derham used a shotgun's noise and several known landmarks around time to measure the time it took for the sound of the blast to be heard from select distances.

Young's Modulus was named after English physicist Thomas Young. In actuality, the concept was developed earlier by physicists Leonhard Euler and Giordano Riccati in the 1720s.

== See also ==

Youngs Modulus: [http://www.physicsbook.gatech.edu/Young%27s_Modulus]
Interatomic Bonds: [http://www.physicsbook.gatech.edu/Length_and_Stiffness_of_an_Interatomic_Bond]

===Further reading===

Further Information can be found on the speed of sound in solids in ''Matter and Interactions, 4th Edition'' by Ruth W. Chabay & Bruce A. Sherwood
===External links===

Internet resources on this topic can be found at:

Engineering Tool Box [http://www.engineeringtoolbox.com/sound-speed-solids-d_713.html]

Hyperphysics [http://hyperphysics.phy-astr.gsu.edu/hbase/sound/souspe2.html]

Potto Project [http://www.potto.org/gasDynamics/node73.html]

NDT Resource Center [https://www.nde-ed.org/EducationResources/CommunityCollege/Ultrasonics/Physics/elasticsolids.htm]

==References==

This section contains the the references used while writing this page

Chart from [http://www.rcgroups.com/forums/attachment.php?attachmentid=3397792]

''Matter and Interactions 4th Edition'' by Chabay and Sherwood

[[Category:Which Category did you place this in?]]

Speed of Sound in Solids

2015-12-06T00:37:07Z

Dpatel322: /* Numerical Example */

This page discusses calculating the speed of sound in various solids and provides examples of such calculations.
Claimed by Dpatel322 @ 12/1

==The Main Idea==

The speed of sound is the speed that sound wave travels through a particular medium. In comparison to air, sound travels considerably faster in solids. The speed that sound travels in various solids depends on the solid's density and elasticity, as these factors effect the ability of the sound waves vibrational energy to transfer across the solid medium.

===A Mathematical Model===

The speed of sound in solids <math> {V_{s}} </math> can be determined by the equation. Young's Modulus is a measure of elasticity of an object, and it can be computed to solve for interatomic values, such as interatomic bond stiffness or interatomic bond length.

<math> {V_{s}} = d* √ (K_{s}/m_{atom}) </math>

<math> d </math> = interatomic bond length

<math> K_{s} </math> = Interatomic bond stiffness

Youngs Modulus = (<math> Y = K_{s}/d </math>)

Youngs Modulus: <math> Y ={\frac{Stress}{Strain}}</math>

<math> Stress = {\frac{F_{tension}}{Area_{Cross Sectional}}} </math>

<math> Strain = {\frac{ΔL_{wire}}{L_{0}}} </math>

===Speeds of Various Compositions===
[[File:speedofsound.jpg]]

==Examples==

Be sure to show all steps in your solution and include diagrams whenever possible

===Theoretical===

Two metal rods are made of different elements. The interatomic spring stiffness of element A is four times larger than the interatomic spring stiffness for element B. The mass of an atom of element A is four times greater than the mass of an atom of element B. The atomic diameters are approximately the same for A and B. What is the ratio of the speed of sound in rod A to the speed of sound in rod B?

Solution: In this situation, the ratio of the speed of sound in rod A to the speed of sound in rod B is 1.

Looking at the formula for computing speed of sound in solids, <math> {V_{s}} = d* √ (K_{s}/m_{atom}) </math>, you see that velocity depends three factors, interatomic stiffness, the mass of one atom, and interatomic bond length. The two rods differences in atomic mass and interatomic stiffness offset each other when the equations are set equal, and the ratio is determined to be 1.

<math> d* √ 4(K_{s}/m_{atom}) = d* √ (K_{s}/4m_{atom}) </math> After simplification <math> V_{s_{1}} = V_{s{2}} </math>

===Numerical Example ===
The Young's Modulus value of silver is 7.75e+10, atomic mass of silver is 108 g/mole, and the density of silver is 10.5 g/cm3. Using this information, calculate the speed of sound in silver.

Solution: The key to solving this problem is to realize the micro-macro connection of Young's Modulus. You are given that Young's Modulus is equal to 7.75e+10, and we know that
Youngs Modulus = (<math> K_{s}/d </math>). In this situation, we need to calculate the interatomic bond length and use it and our Young's Modulus value to determine our interatomic stiffness.

To solve for ''d'', we use the given density of silver (10.5 g/cm3). Using the basic equation for volume in relation to density and mass (<math> V=m*d</math>), we can find ''d'', since ''d'' is equal to the cube root of volume.

Once ''d'' is solved for, it can be plugged back into the the equation <math> Y = K_{s}/d </math> to solve for <math> K_{s} </math>

Now, we have solved for both interatomic bond length and stiffness. The only quantity in the final speed of sound equation we need is the mass of one atom, which can be determined using Avogardro's number and the atomic mass. <math> m_{atom} = </math> atomic mass / <math> 6.022e23 </math>

==Connectedness==
The computation of speed of sound in solids is dependent on a mass' interatomic properties, such as interatomic bond length. I find it interesting when a object's interatomic properties determine its functionality on a larger scale. In the case of speed of sound in solids, the objects elasticity depends on the interatomic bond length.

While the computation of speed of sound in solids may not seem related to Industrial Engineering, it has clear implications in the process of choosing building materials, which is a notable section of industrial engineering. For example, if you are planning to build something soundproof, it would be optimal to choose a solid with a very low speed of sound velocity.

The industrial applications in terms of construction are vast. An objects ability to block/allow sound waves through it is very important. Of course, insulation materials and sound proof wall materials come to thought at first. However, in some cases, contractors need to build structures that allow sound to travel through, in which they would choose solid materials that correlate with high speeds of sound.

==History==

The speed of sound in air was first measured by Sir Isaac Newton, and first correctly computed by Pierre-Simon Laplace in 1816. Before this precise measurement, attempts had been made across Europe during the 1700s, most famously Reverend William Derham's experiment in 1709 across the town of Upminister, England. Reverend Derham used a shotgun's noise and several known landmarks around time to measure the time it took for the sound of the blast to be heard from select distances.

Young's Modulus was named after English physicist Thomas Young. In actuality, the concept was developed earlier by physicists Leonhard Euler and Giordano Riccati in the 1720s.

== See also ==

Youngs Modulus: [http://www.physicsbook.gatech.edu/Young%27s_Modulus]
Interatomic Bonds: [http://www.physicsbook.gatech.edu/Length_and_Stiffness_of_an_Interatomic_Bond]

===Further reading===

Further Information can be found on the speed of sound in solids in ''Matter and Interactions, 4th Edition'' by Ruth W. Chabay & Bruce A. Sherwood
===External links===

Internet resources on this topic can be found at:

Engineering Tool Box [http://www.engineeringtoolbox.com/sound-speed-solids-d_713.html]

Hyperphysics [http://hyperphysics.phy-astr.gsu.edu/hbase/sound/souspe2.html]

Potto Project [http://www.potto.org/gasDynamics/node73.html]

NDT Resource Center [https://www.nde-ed.org/EducationResources/CommunityCollege/Ultrasonics/Physics/elasticsolids.htm]

==References==

This section contains the the references used while writing this page

Chart from [http://www.rcgroups.com/forums/attachment.php?attachmentid=3397792]

''Matter and Interactions 4th Edition'' by Chabay and Sherwood

[[Category:Which Category did you place this in?]]

Speed of Sound in Solids

2015-12-06T00:00:51Z

Dpatel322:

This page discusses calculating the speed of sound in various solids and provides examples of such calculations.
Claimed by Dpatel322 @ 12/1

==The Main Idea==

The speed of sound is the speed that sound wave travels through a particular medium. In comparison to air, sound travels considerably faster in solids. The speed that sound travels in various solids depends on the solid's density and elasticity, as these factors effect the ability of the sound waves vibrational energy to transfer across the solid medium.

===A Mathematical Model===

The speed of sound in solids <math> {V_{s}} </math> can be determined by the equation. Young's Modulus is a measure of elasticity of an object, and it can be computed to solve for interatomic values, such as interatomic bond stiffness or interatomic bond length.

<math> {V_{s}} = d* √ (K_{s}/m_{atom}) </math>

<math> d </math> = interatomic bond length

<math> K_{s} </math> = Interatomic bond stiffness

Youngs Modulus = (<math> Y = K_{s}/d </math>)

Youngs Modulus: <math> Y ={\frac{Stress}{Strain}}</math>

<math> Stress = {\frac{F_{tension}}{Area_{Cross Sectional}}} </math>

<math> Strain = {\frac{ΔL_{wire}}{L_{0}}} </math>

===Speeds of Various Compositions===
[[File:speedofsound.jpg]]

==Examples==

Be sure to show all steps in your solution and include diagrams whenever possible

===Theoretical===

Two metal rods are made of different elements. The interatomic spring stiffness of element A is four times larger than the interatomic spring stiffness for element B. The mass of an atom of element A is four times greater than the mass of an atom of element B. The atomic diameters are approximately the same for A and B. What is the ratio of the speed of sound in rod A to the speed of sound in rod B?

Solution: In this situation, the ratio of the speed of sound in rod A to the speed of sound in rod B is 1.

Looking at the formula for computing speed of sound in solids, <math> {V_{s}} = d* √ (K_{s}/m_{atom}) </math>, you see that velocity depends three factors, interatomic stiffness, the mass of one atom, and interatomic bond length. The two rods differences in atomic mass and interatomic stiffness offset each other when the equations are set equal, and the ratio is determined to be 1.

<math> d* √ 4(K_{s}/m_{atom}) = d* √ (K_{s}/4m_{atom}) </math> After simplification <math> V_{s_{1}} = V_{s{2}} </math>

===Numerical Example ===
The Young's Modulus value of silver is 7.75e+10, atomic mass of silver is 108 g/mole, and the density of silver is 10.5 g/cm3. Using this information, calculate the speed of sound in silver.

Solution: The key to solving this problem is to realize the micro-macro connection of Young's Modulus. You are given that Young's Modulus is equal to 7.75e+10, and we know that
Youngs Modulus = (<math> K_{s}/d </math>). In this situation, we need to calculate the interatomic bond length and use it and our Young's Modulus value to determine our interatomic stiffness.

To solve for ''d'', we use the given density of silver (10.5 g/cm3). Using the basic equation for volume in relation to density and mass, we can find ''d'', since "d" is equal to the cube root of volume. In this case, volume is equal to

==Connectedness==
The computation of speed of sound in solids is dependent on a mass' interatomic properties, such as interatomic bond length. I find it interesting when a object's interatomic properties determine its functionality on a larger scale. In the case of speed of sound in solids, the objects elasticity depends on the interatomic bond length.

While the computation of speed of sound in solids may not seem related to Industrial Engineering, it has clear implications in the process of choosing building materials, which is a notable section of industrial engineering. For example, if you are planning to build something soundproof, it would be optimal to choose a solid with a very low speed of sound velocity.

The industrial applications in terms of construction are vast. An objects ability to block/allow sound waves through it is very important. Of course, insulation materials and sound proof wall materials come to thought at first. However, in some cases, contractors need to build structures that allow sound to travel through, in which they would choose solid materials that correlate with high speeds of sound.

==History==

The speed of sound in air was first measured by Sir Isaac Newton, and first correctly computed by Pierre-Simon Laplace in 1816. Before this precise measurement, attempts had been made across Europe during the 1700s, most famously Reverend William Derham's experiment in 1709 across the town of Upminister, England. Reverend Derham used a shotgun's noise and several known landmarks around time to measure the time it took for the sound of the blast to be heard from select distances.

Young's Modulus was named after English physicist Thomas Young. In actuality, the concept was developed earlier by physicists Leonhard Euler and Giordano Riccati in the 1720s.

== See also ==

Youngs Modulus: [http://www.physicsbook.gatech.edu/Young%27s_Modulus]
Interatomic Bonds: [http://www.physicsbook.gatech.edu/Length_and_Stiffness_of_an_Interatomic_Bond]

===Further reading===

Further Information can be found on the speed of sound in solids in ''Matter and Interactions, 4th Edition'' by Ruth W. Chabay & Bruce A. Sherwood
===External links===

Internet resources on this topic can be found at:

Engineering Tool Box [http://www.engineeringtoolbox.com/sound-speed-solids-d_713.html]

Hyperphysics [http://hyperphysics.phy-astr.gsu.edu/hbase/sound/souspe2.html]

Potto Project [http://www.potto.org/gasDynamics/node73.html]

NDT Resource Center [https://www.nde-ed.org/EducationResources/CommunityCollege/Ultrasonics/Physics/elasticsolids.htm]

==References==

This section contains the the references used while writing this page

Chart from [http://www.rcgroups.com/forums/attachment.php?attachmentid=3397792]

''Matter and Interactions 4th Edition'' by Chabay and Sherwood

[[Category:Which Category did you place this in?]]

Speed of Sound in Solids

2015-12-05T23:54:20Z

Dpatel322: /* Numerical Example */

This page discusses calculating the speed of sound in various solids and provides examples of such calculations.
Claimed by Dpatel322 @ 12/1

==The Main Idea==

The speed of sound is the speed that sound wave travels through a particular medium. In comparison to air, sound travels considerably faster in solids. The speed that sound travels in various solids depends on the solid's density and elasticity, as these factors effect the ability of the sound waves vibrational energy to transfer across the solid medium.

===A Mathematical Model===

The speed of sound in solids <math> {V_{s}} </math> can be determined by the equation. Young's Modulus is a measure of elasticity of an object, and it can be computed to solve for interatomic values, such as interatomic bond stiffness or interatomic bond length.

<math> {V_{s}} = d* √ (K_{s}/m_{atom}) </math>

<math> d </math> = interatomic bond length

<math> K_{s} </math> = Interatomic bond stiffness

Youngs Modulus = (<math> Y = K_{s}/d </math>)

Youngs Modulus: <math> Y ={\frac{Stress}{Strain}}</math>

<math> Stress = {\frac{F_{tension}}{Area_{Cross Sectional}}} </math>

<math> Strain = {\frac{ΔL_{wire}}{L_{0}}} </math>

===Speeds of Various Compositions===
[[File:speedofsound.jpg]]

==Examples==

Be sure to show all steps in your solution and include diagrams whenever possible

===Theoretical===

Two metal rods are made of different elements. The interatomic spring stiffness of element A is four times larger than the interatomic spring stiffness for element B. The mass of an atom of element A is four times greater than the mass of an atom of element B. The atomic diameters are approximately the same for A and B. What is the ratio of the speed of sound in rod A to the speed of sound in rod B?

Solution: In this situation, the ratio of the speed of sound in rod A to the speed of sound in rod B is 1.

Looking at the formula for computing speed of sound in solids, <math> {V_{s}} = d* √ (K_{s}/m_{atom}) </math>, you see that velocity depends three factors, interatomic stiffness, the mass of one atom, and interatomic bond length. The two rods differences in atomic mass and interatomic stiffness offset each other when the equations are set equal, and the ratio is determined to be 1.

<math> d* √ 4(K_{s}/m_{atom}) = d* √ (K_{s}/4m_{atom}) </math> After simplification <math> V_{s_{1}} = V_{s{2}} </math>

===Numerical Example ===
The Young's Modulus value of silver is 7.75e+10, atomic mass of silver is 108 g/mole, and the density of silver is 10.5 g/cm3. Using this information, calculate the speed of sound in silver.

Solution: The key to solving this problem is to realize the micro-macro connection of Young's Modulus. You are given that Young's Modulus is equal to 7.75e+10, and we know that

==Connectedness==
The computation of speed of sound in solids is dependent on a mass' interatomic properties, such as interatomic bond length. I find it interesting when a object's interatomic properties determine its functionality on a larger scale. In the case of speed of sound in solids, the objects elasticity depends on the interatomic bond length.

While the computation of speed of sound in solids may not seem related to Industrial Engineering, it has clear implications in the process of choosing building materials, which is a notable section of industrial engineering. For example, if you are planning to build something soundproof, it would be optimal to choose a solid with a very low speed of sound velocity.

The industrial applications in terms of construction are vast. An objects ability to block/allow sound waves through it is very important. Of course, insulation materials and sound proof wall materials come to thought at first. However, in some cases, contractors need to build structures that allow sound to travel through, in which they would choose solid materials that correlate with high speeds of sound.

==History==

The speed of sound in air was first measured by Sir Isaac Newton, and first correctly computed by Pierre-Simon Laplace in 1816. Before this precise measurement, attempts had been made across Europe during the 1700s, most famously Reverend William Derham's experiment in 1709 across the town of Upminister, England. Reverend Derham used a shotgun's noise and several known landmarks around time to measure the time it took for the sound of the blast to be heard from select distances.

Young's Modulus was named after English physicist Thomas Young. In actuality, the concept was developed earlier by physicists Leonhard Euler and Giordano Riccati in the 1720s.

== See also ==

Youngs Modulus: [http://www.physicsbook.gatech.edu/Young%27s_Modulus]
Interatomic Bonds: [http://www.physicsbook.gatech.edu/Length_and_Stiffness_of_an_Interatomic_Bond]

===Further reading===

Further Information can be found on the speed of sound in solids in ''Matter and Interactions, 4th Edition'' by Ruth W. Chabay & Bruce A. Sherwood
===External links===

Internet resources on this topic can be found at:

Engineering Tool Box [http://www.engineeringtoolbox.com/sound-speed-solids-d_713.html]

Hyperphysics [http://hyperphysics.phy-astr.gsu.edu/hbase/sound/souspe2.html]

Potto Project [http://www.potto.org/gasDynamics/node73.html]

NDT Resource Center [https://www.nde-ed.org/EducationResources/CommunityCollege/Ultrasonics/Physics/elasticsolids.htm]

==References==

This section contains the the references used while writing this page

Chart from [http://www.rcgroups.com/forums/attachment.php?attachmentid=3397792]

''Matter and Interactions 4th Edition'' by Chabay and Sherwood

[[Category:Which Category did you place this in?]]

Speed of Sound in Solids

2015-12-05T23:49:24Z

Dpatel322: /* Numerical Example 2 */

This page discusses calculating the speed of sound in various solids and provides examples of such calculations.
Claimed by Dpatel322 @ 12/1

==The Main Idea==

The speed of sound is the speed that sound wave travels through a particular medium. In comparison to air, sound travels considerably faster in solids. The speed that sound travels in various solids depends on the solid's density and elasticity, as these factors effect the ability of the sound waves vibrational energy to transfer across the solid medium.

===A Mathematical Model===

The speed of sound in solids <math> {V_{s}} </math> can be determined by the equation. Young's Modulus is a measure of elasticity of an object, and it can be computed to solve for interatomic values, such as interatomic bond stiffness or interatomic bond length.

<math> {V_{s}} = d* √ (K_{s}/m_{atom}) </math>

<math> d </math> = interatomic bond length

<math> K_{s} </math> = Interatomic bond stiffness

Youngs Modulus = (<math> Y = K_{s}/d </math>)

Youngs Modulus: <math> Y ={\frac{Stress}{Strain}}</math>

<math> Stress = {\frac{F_{tension}}{Area_{Cross Sectional}}} </math>

<math> Strain = {\frac{ΔL_{wire}}{L_{0}}} </math>

===Speeds of Various Compositions===
[[File:speedofsound.jpg]]

==Examples==

Be sure to show all steps in your solution and include diagrams whenever possible

===Theoretical===

Two metal rods are made of different elements. The interatomic spring stiffness of element A is four times larger than the interatomic spring stiffness for element B. The mass of an atom of element A is four times greater than the mass of an atom of element B. The atomic diameters are approximately the same for A and B. What is the ratio of the speed of sound in rod A to the speed of sound in rod B?

Solution: In this situation, the ratio of the speed of sound in rod A to the speed of sound in rod B is 1.

Looking at the formula for computing speed of sound in solids, <math> {V_{s}} = d* √ (K_{s}/m_{atom}) </math>, you see that velocity depends three factors, interatomic stiffness, the mass of one atom, and interatomic bond length. The two rods differences in atomic mass and interatomic stiffness offset each other when the equations are set equal, and the ratio is determined to be 1.

<math> d* √ 4(K_{s}/m_{atom}) = d* √ (K_{s}/4m_{atom}) </math> After simplification <math> V_{s_{1}} = V_{s{2}} </math>

===Numerical Example ===
The Young's Modulus value of silver is 7.75e+10, atomic mass of silver is 108 g/mole, and the density of silver is 10.5 g/cm3. Using this information, calculate the speed of sound in silver.

==Connectedness==
The computation of speed of sound in solids is dependent on a mass' interatomic properties, such as interatomic bond length. I find it interesting when a object's interatomic properties determine its functionality on a larger scale. In the case of speed of sound in solids, the objects elasticity depends on the interatomic bond length.

While the computation of speed of sound in solids may not seem related to Industrial Engineering, it has clear implications in the process of choosing building materials, which is a notable section of industrial engineering. For example, if you are planning to build something soundproof, it would be optimal to choose a solid with a very low speed of sound velocity.

The industrial applications in terms of construction are vast. An objects ability to block/allow sound waves through it is very important. Of course, insulation materials and sound proof wall materials come to thought at first. However, in some cases, contractors need to build structures that allow sound to travel through, in which they would choose solid materials that correlate with high speeds of sound.

==History==

The speed of sound in air was first measured by Sir Isaac Newton, and first correctly computed by Pierre-Simon Laplace in 1816. Before this precise measurement, attempts had been made across Europe during the 1700s, most famously Reverend William Derham's experiment in 1709 across the town of Upminister, England. Reverend Derham used a shotgun's noise and several known landmarks around time to measure the time it took for the sound of the blast to be heard from select distances.

Young's Modulus was named after English physicist Thomas Young. In actuality, the concept was developed earlier by physicists Leonhard Euler and Giordano Riccati in the 1720s.

== See also ==

Youngs Modulus: [http://www.physicsbook.gatech.edu/Young%27s_Modulus]
Interatomic Bonds: [http://www.physicsbook.gatech.edu/Length_and_Stiffness_of_an_Interatomic_Bond]

===Further reading===

Further Information can be found on the speed of sound in solids in ''Matter and Interactions, 4th Edition'' by Ruth W. Chabay & Bruce A. Sherwood
===External links===

Internet resources on this topic can be found at:

Engineering Tool Box [http://www.engineeringtoolbox.com/sound-speed-solids-d_713.html]

Hyperphysics [http://hyperphysics.phy-astr.gsu.edu/hbase/sound/souspe2.html]

Potto Project [http://www.potto.org/gasDynamics/node73.html]

NDT Resource Center [https://www.nde-ed.org/EducationResources/CommunityCollege/Ultrasonics/Physics/elasticsolids.htm]

==References==

This section contains the the references used while writing this page

Chart from [http://www.rcgroups.com/forums/attachment.php?attachmentid=3397792]

''Matter and Interactions 4th Edition'' by Chabay and Sherwood

[[Category:Which Category did you place this in?]]

Speed of Sound in Solids

2015-12-05T23:49:11Z

Dpatel322: /* Numerical Example 1 */

This page discusses calculating the speed of sound in various solids and provides examples of such calculations.
Claimed by Dpatel322 @ 12/1

==The Main Idea==

The speed of sound is the speed that sound wave travels through a particular medium. In comparison to air, sound travels considerably faster in solids. The speed that sound travels in various solids depends on the solid's density and elasticity, as these factors effect the ability of the sound waves vibrational energy to transfer across the solid medium.

===A Mathematical Model===

The speed of sound in solids <math> {V_{s}} </math> can be determined by the equation. Young's Modulus is a measure of elasticity of an object, and it can be computed to solve for interatomic values, such as interatomic bond stiffness or interatomic bond length.

<math> {V_{s}} = d* √ (K_{s}/m_{atom}) </math>

<math> d </math> = interatomic bond length

<math> K_{s} </math> = Interatomic bond stiffness

Youngs Modulus = (<math> Y = K_{s}/d </math>)

Youngs Modulus: <math> Y ={\frac{Stress}{Strain}}</math>

<math> Stress = {\frac{F_{tension}}{Area_{Cross Sectional}}} </math>

<math> Strain = {\frac{ΔL_{wire}}{L_{0}}} </math>

===Speeds of Various Compositions===
[[File:speedofsound.jpg]]

==Examples==

Be sure to show all steps in your solution and include diagrams whenever possible

===Theoretical===

Two metal rods are made of different elements. The interatomic spring stiffness of element A is four times larger than the interatomic spring stiffness for element B. The mass of an atom of element A is four times greater than the mass of an atom of element B. The atomic diameters are approximately the same for A and B. What is the ratio of the speed of sound in rod A to the speed of sound in rod B?

Solution: In this situation, the ratio of the speed of sound in rod A to the speed of sound in rod B is 1.

Looking at the formula for computing speed of sound in solids, <math> {V_{s}} = d* √ (K_{s}/m_{atom}) </math>, you see that velocity depends three factors, interatomic stiffness, the mass of one atom, and interatomic bond length. The two rods differences in atomic mass and interatomic stiffness offset each other when the equations are set equal, and the ratio is determined to be 1.

<math> d* √ 4(K_{s}/m_{atom}) = d* √ (K_{s}/4m_{atom}) </math> After simplification <math> V_{s_{1}} = V_{s{2}} </math>

===Numerical Example 2===
The Young's Modulus value of silver is 7.75e+10, atomic mass of silver is 108 g/mole, and the density of silver is 10.5 g/cm3. Using this information, calculate the speed of sound in silver.

==Connectedness==
The computation of speed of sound in solids is dependent on a mass' interatomic properties, such as interatomic bond length. I find it interesting when a object's interatomic properties determine its functionality on a larger scale. In the case of speed of sound in solids, the objects elasticity depends on the interatomic bond length.

While the computation of speed of sound in solids may not seem related to Industrial Engineering, it has clear implications in the process of choosing building materials, which is a notable section of industrial engineering. For example, if you are planning to build something soundproof, it would be optimal to choose a solid with a very low speed of sound velocity.

The industrial applications in terms of construction are vast. An objects ability to block/allow sound waves through it is very important. Of course, insulation materials and sound proof wall materials come to thought at first. However, in some cases, contractors need to build structures that allow sound to travel through, in which they would choose solid materials that correlate with high speeds of sound.

==History==

The speed of sound in air was first measured by Sir Isaac Newton, and first correctly computed by Pierre-Simon Laplace in 1816. Before this precise measurement, attempts had been made across Europe during the 1700s, most famously Reverend William Derham's experiment in 1709 across the town of Upminister, England. Reverend Derham used a shotgun's noise and several known landmarks around time to measure the time it took for the sound of the blast to be heard from select distances.

Young's Modulus was named after English physicist Thomas Young. In actuality, the concept was developed earlier by physicists Leonhard Euler and Giordano Riccati in the 1720s.

== See also ==

Youngs Modulus: [http://www.physicsbook.gatech.edu/Young%27s_Modulus]
Interatomic Bonds: [http://www.physicsbook.gatech.edu/Length_and_Stiffness_of_an_Interatomic_Bond]

===Further reading===

Further Information can be found on the speed of sound in solids in ''Matter and Interactions, 4th Edition'' by Ruth W. Chabay & Bruce A. Sherwood
===External links===

Internet resources on this topic can be found at:

Engineering Tool Box [http://www.engineeringtoolbox.com/sound-speed-solids-d_713.html]

Hyperphysics [http://hyperphysics.phy-astr.gsu.edu/hbase/sound/souspe2.html]

Potto Project [http://www.potto.org/gasDynamics/node73.html]

NDT Resource Center [https://www.nde-ed.org/EducationResources/CommunityCollege/Ultrasonics/Physics/elasticsolids.htm]

==References==

This section contains the the references used while writing this page

Chart from [http://www.rcgroups.com/forums/attachment.php?attachmentid=3397792]

''Matter and Interactions 4th Edition'' by Chabay and Sherwood

[[Category:Which Category did you place this in?]]

Speed of Sound in Solids

2015-12-05T20:39:05Z

Dpatel322: Created page with "This page discusses calculating the speed of sound in various solids and provides examples of such calculations. Claimed by Dpatel322 @ 12/1 ==The Main Idea== The speed of s..."

This page discusses calculating the speed of sound in various solids and provides examples of such calculations.
Claimed by Dpatel322 @ 12/1

==The Main Idea==

The speed of sound is the speed that sound wave travels through a particular medium. In comparison to air, sound travels considerably faster in solids. The speed that sound travels in various solids depends on the solid's density and elasticity, as these factors effect the ability of the sound waves vibrational energy to transfer across the solid medium.

===A Mathematical Model===

The speed of sound in solids <math> {V_{s}} </math> can be determined by the equation. Young's Modulus is a measure of elasticity of an object, and it can be computed to solve for interatomic values, such as interatomic bond stiffness or interatomic bond length.

<math> {V_{s}} = d* √ (K_{s}/m_{atom}) </math>

<math> d </math> = interatomic bond length

<math> K_{s} </math> = Interatomic bond stiffness

Youngs Modulus = (<math> Y = K_{s}/d </math>)

Youngs Modulus: <math> Y ={\frac{Stress}{Strain}}</math>

<math> Stress = {\frac{F_{tension}}{Area_{Cross Sectional}}} </math>

<math> Strain = {\frac{ΔL_{wire}}{L_{0}}} </math>

===Speeds of Various Compositions===
[[File:speedofsound.jpg]]

==Examples==

Be sure to show all steps in your solution and include diagrams whenever possible

===Theoretical===

Two metal rods are made of different elements. The interatomic spring stiffness of element A is four times larger than the interatomic spring stiffness for element B. The mass of an atom of element A is four times greater than the mass of an atom of element B. The atomic diameters are approximately the same for A and B. What is the ratio of the speed of sound in rod A to the speed of sound in rod B?

Solution: In this situation, the ratio of the speed of sound in rod A to the speed of sound in rod B is 1.

Looking at the formula for computing speed of sound in solids, <math> {V_{s}} = d* √ (K_{s}/m_{atom}) </math>, you see that velocity depends three factors, interatomic stiffness, the mass of one atom, and interatomic bond length. The two rods differences in atomic mass and interatomic stiffness offset each other when the equations are set equal, and the ratio is determined to be 1.

<math> d* √ 4(K_{s}/m_{atom}) = d* √ (K_{s}/4m_{atom}) </math> After simplification <math> V_{s_{1}} = V_{s{2}} </math>

===Numerical Example 1===

A certain metal with atomic mass 2.7 × 10−25 kg has an interatomic bond with length 2.3 × 10−10 m and stiffness 46 N/m. What is the speed of sound in a rod made of this metal?

Solution:

===Numerical Example 2===
The Young's Modulus value of silver is 7.75e+10, atomic mass of silver is 108 g/mole, and the density of silver is 10.5 g/cm3. Using this information, calculate the speed of sound in silver.

==Connectedness==
The computation of speed of sound in solids is dependent on a mass' interatomic properties, such as interatomic bond length. I find it interesting when a object's interatomic properties determine its functionality on a larger scale. In the case of speed of sound in solids, the objects elasticity depends on the interatomic bond length.

While the computation of speed of sound in solids may not seem related to Industrial Engineering, it has clear implications in the process of choosing building materials, which is a notable section of industrial engineering. For example, if you are planning to build something soundproof, it would be optimal to choose a solid with a very low speed of sound velocity.

The industrial applications in terms of construction are vast. An objects ability to block/allow sound waves through it is very important. Of course, insulation materials and sound proof wall materials come to thought at first. However, in some cases, contractors need to build structures that allow sound to travel through, in which they would choose solid materials that correlate with high speeds of sound.

==History==

The speed of sound in air was first measured by Sir Isaac Newton, and first correctly computed by Pierre-Simon Laplace in 1816. Before this precise measurement, attempts had been made across Europe during the 1700s, most famously Reverend William Derham's experiment in 1709 across the town of Upminister, England. Reverend Derham used a shotgun's noise and several known landmarks around time to measure the time it took for the sound of the blast to be heard from select distances.

Young's Modulus was named after English physicist Thomas Young. In actuality, the concept was developed earlier by physicists Leonhard Euler and Giordano Riccati in the 1720s.

== See also ==

Youngs Modulus: [http://www.physicsbook.gatech.edu/Young%27s_Modulus]
Interatomic Bonds: [http://www.physicsbook.gatech.edu/Length_and_Stiffness_of_an_Interatomic_Bond]

===Further reading===

Further Information can be found on the speed of sound in solids in ''Matter and Interactions, 4th Edition'' by Ruth W. Chabay & Bruce A. Sherwood
===External links===

Internet resources on this topic can be found at:

Engineering Tool Box [http://www.engineeringtoolbox.com/sound-speed-solids-d_713.html]

Hyperphysics [http://hyperphysics.phy-astr.gsu.edu/hbase/sound/souspe2.html]

Potto Project [http://www.potto.org/gasDynamics/node73.html]

NDT Resource Center [https://www.nde-ed.org/EducationResources/CommunityCollege/Ultrasonics/Physics/elasticsolids.htm]

==References==

This section contains the the references used while writing this page

Chart from [http://www.rcgroups.com/forums/attachment.php?attachmentid=3397792]

''Matter and Interactions 4th Edition'' by Chabay and Sherwood

[[Category:Which Category did you place this in?]]

Main Page

2015-12-05T20:38:41Z

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__NOTOC__
Welcome to the Georgia Tech Wiki for Intro Physics. This resources was created so that students can contribute and curate content to help those with limited or no access to a textbook. When reading this website, please correct any errors you may come across. If you read something that isn't clear, please consider revising it!

Looking to make a contribution?
#Pick a specific topic from intro physics
#Add that topic, as a link to a new page, under the appropriate category listed below by editing this page.
#Copy and paste the default [[Template]] into your new page and start editing.

Please remember that this is not a textbook and you are not limited to expressing your ideas with only text and equations. Whenever possible embed: pictures, videos, diagrams, simulations, computational models (e.g. Glowscript), and whatever content you think makes learning physics easier for other students.

== Source Material ==
All of the content added to this resource must be in the public domain or similar free resource. If you are unsure about a source, contact the original author for permission. That said, there is a surprisingly large amount of introductory physics content scattered across the web. Here is an incomplete list of intro physics resources (please update as needed).
* A physics resource written by experts for an expert audience [https://en.wikipedia.org/wiki/Portal:Physics Physics Portal]
* A wiki book on modern physics [https://en.wikibooks.org/wiki/Modern_Physics Modern Physics Wiki]
* The MIT open courseware for intro physics [http://ocw.mit.edu/resources/res-8-002-a-wikitextbook-for-introductory-mechanics-fall-2009/index.htm MITOCW Wiki]
* An online concept map of intro physics [http://hyperphysics.phy-astr.gsu.edu/hbase/hph.html HyperPhysics]
* Interactive physics simulations [https://phet.colorado.edu/en/simulations/category/physics PhET]
* OpenStax algebra based intro physics textbook [https://openstaxcollege.org/textbooks/college-physics College Physics]
* The Open Source Physics project is a collection of online physics resources [http://www.opensourcephysics.org/ OSP]
* A resource guide compiled by the [http://www.aapt.org/ AAPT] for educators [http://www.compadre.org/ ComPADRE]

== Organizing Categories ==
These are the broad, overarching categories, that we cover in two semester of introductory physics. You can add subcategories or make a new category as needed. A single topic should direct readers to a page in one of these catagories.

<div class="toccolours mw-collapsible mw-collapsed">
===Interactions===
<div class="mw-collapsible-content">
*[[Kinds of Matter]]
**[[Ball and Spring Model of Matter]]
*[[Detecting Interactions]]
*[[Escape Velocity]]
*[[Fundamental Interactions]]
*[[Determinism]]
*[[System & Surroundings]]
*[[Free Body Diagram]]
*[[Newton's First Law of Motion]]
*[[Newton's Second Law of Motion]]
*[[Newton's Third Law of Motion]]
*[[Gravitational Force]]
*[[Electric Force]]
*[[Conservation of Energy]]
*[[Conservation of Charge]]
*[[Terminal Speed]]
*[[Simple Harmonic Motion]]
*[[Speed and Velocity]]
*[[Electric Polarization]]
*[[Perpetual Freefall (Orbit)]]
*[[2-Dimensional Motion]]
*[[Center of Mass]]
*[[Reaction Time]]
*[[Time Dilation]]
</div>
</div>

<div class="toccolours mw-collapsible mw-collapsed">

===Modeling with VPython===
<div class="mw-collapsible-content">
*[[VPython]]
*[[VPython basics]]
*[[VPython Common Errors and Troubleshooting]]
*[[VPython Functions]]
*[[VPython Lists]]
*[[VPython Multithreading]]
*[[VPython Animation]]
</div>
</div>

<div class="toccolours mw-collapsible mw-collapsed">

===Theory===
<div class="mw-collapsible-content">
*[[Einstein's Theory of Special Relativity]]
*[[Einstein's Theory of General Relativity]]
*[[Quantum Theory]]
*[[Maxwell's Electromagnetic Theory]]
*[[Atomic Theory]]
*[[String Theory]]
*[[Elementary Particles and Particle Physics Theory]]
*[[Law of Gravitation]]
*[[Newton's Laws]]
</div>
</div>

<div class="toccolours mw-collapsible mw-collapsed">

===Notable Scientists===
<div class="mw-collapsible-content">
*[[Alexei Alexeyevich Abrikosov]]
*[[Christian Doppler]]
*[[Albert Einstein]]
*[[Ernest Rutherford]]
*[[Joseph Henry]]
*[[Michael Faraday]]
*[[J.J. Thomson]]
*[[James Maxwell]]
*[[Robert Hooke]]
*[[Carl Friedrich Gauss]]
*[[Nikola Tesla]]
*[[Andre Marie Ampere]]
*[[Sir Isaac Newton]]
*[[J. Robert Oppenheimer]]
*[[Oliver Heaviside]]
*[[Rosalind Franklin]]
*[[Enrico Fermi]]
*[[Robert J. Van de Graaff]]
*[[Charles de Coulomb]]
*[[Hans Christian Ørsted]]
*[[Philo Farnsworth]]
*[[Niels Bohr]]
*[[Georg Ohm]]
*[[Galileo Galilei]]
*[[Gustav Kirchhoff]]
*[[Max Planck]]
*[[Heinrich Hertz]]
*[[Edwin Hall]]
*[[James Watt]]
*[[Count Alessandro Volta]]
*[[Josiah Willard Gibbs]]
*[[Richard Phillips Feynman]]
*[[Sir David Brewster]]
*[[Daniel Bernoulli]]
*[[William Thomson]]
*[[Leonhard Euler]]
*[[Robert Fox Bacher]]
*[[Stephen Hawking]]
*[[Amedeo Avogadro]]
*[[Wilhelm Conrad Roentgen]]
*[[Pierre Laplace]]
*[[Thomas Edison]]
*[[Hendrik Lorentz]]
*[[Jean-Baptiste Biot]]
*[[Lise Meitner]]
*[[Lisa Randall]]
*[[Felix Savart]]
*[[Heinrich Lenz]]
*[[Max Born]]
*[[Archimedes]]
*[[Jean Baptiste Biot]]
*[[Carl Sagan]]
*[[Eugene Wigner]]
*[[Marie Curie]]
*[[Pierre Curie]]
*[[Werner Heisenberg]]
*[[Johannes Diderik van der Waals]]
*[[Louis de Broglie]]
*[[Aristotle]]
*[[Émilie du Châtelet]]
*[[Blaise Pascal]]
*[[Siméon Denis Poisson]]
*[[Benjamin Franklin]]
*[[James Chadwick]]
*[[Henry Cavendish]]
*[[Thomas Young]]
*[[James Prescott Joule]]
*[[John Bardeen]]
*[[Leo Baekeland]]
*[[Alhazen]]
*[[Willebrord Snell]]
*[[Fritz Walther Meissner]]
*[[Johannes Kepler]]
*[[Johann Wilhelm Ritter]]
*[[Philipp Lenard]]
*[[Robert A. Millikan]]
*[[Joseph Louis Gay-Lussac]]
*[[Guglielmo Marconi]]
*[[William Lawrence Bragg]]
*[[Robert Goddard]]
*[[Léon Foucault]]
*[[Henri Poincaré]]
*[[Steven Weinberg]]
*[[Arthur Compton]]
*[[Pythagoras of Samos]]
*[[Subrahmanyan Chandrasekhar]]
*[[Wilhelm Eduard Weber]]
*[[Edmond Becquerel]]
*[[Joseph Rotblat]]
*[[Carl David Anderson]]
*[[Hermann von Helmholtz]]
*[[Nicolas Leonard Sadi Carnot]]
*[[Wallace Carothers]]
*[[David J. Wineland]]
*[[Rudolf Clausius]]
*[[Edward L. Norton]]
*[[Shuji Nakamura]]
*[[Pierre Laplace Pt. 2]]
*[[William B. Shockley]]
*[[Osborne Reynolds]]
*[[Alexander Graham Bell]]
*[[Hans Bethe]]

</div>
</div>

<div class="toccolours mw-collapsible mw-collapsed">

===Properties of Matter===
<div class="mw-collapsible-content">
*[[Mass]]
*[[Velocity]]
*[[Relative Velocity]]
*[[Density]]
*[[Charge]]
*[[Spin]]
*[[SI Units]]
*[[Heat Capacity]]
*[[Specific Heat]]
*[[Wavelength]]
*[[Conductivity]]
*[[Malleability]]
*[[Weight]]
*[[Boiling Point]]
*[[Melting Point]]
*[[Inertia]]
*[[Non-Newtonian Fluids]]
*[[Ferrofluids]]
*[[Color]]
*[[Temperature]]
</div>
</div>

<div class="toccolours mw-collapsible mw-collapsed">

===Contact Interactions===
<div class="mw-collapsible-content">
* [[Young's Modulus]]
* [[Friction]]
* [[Tension]]
* [[Hooke's Law]]
*[[Centripetal Force and Curving Motion]]
*[[Compression or Normal Force]]
* [[Length and Stiffness of an Interatomic Bond]]
* [[Speed of Sound in Solids]]
* [[Iterative Prediction of Spring-Mass System]]
</div>
</div>

<div class="toccolours mw-collapsible mw-collapsed">

===Momentum===
<div class="mw-collapsible-content">
* [[Vectors]]
* [[Kinematics]]
* [[Conservation of Momentum]]
* [[Predicting Change in multiple dimensions]]
* [[Derivation of the Momentum Principle]]
* [[Momentum Principle]]
* [[Impulse Momentum]]
* [[Curving Motion]]
* [[Projectile Motion]]
* [[Multi-particle Analysis of Momentum]]
* [[Iterative Prediction]]
* [[Analytical Prediction]]
* [[Newton's Laws and Linear Momentum]]
* [[Net Force]]
* [[Center of Mass]]
* [[Momentum at High Speeds]]
* [[Change in Momentum in Time for Curving Motion]]
* [[Momentum with respect to external Forces]]
</div>
</div>

<div class="toccolours mw-collapsible mw-collapsed">

===Angular Momentum===
<div class="mw-collapsible-content">
* [[The Moments of Inertia]]
* [[Moment of Inertia for a cylinder]]
* [[Rotation]]
* [[Torque]]
* [[Systems with Zero Torque]]
* [[Systems with Nonzero Torque]]
* [[Torque vs Work]]
* [[Angular Impulse]]
* [[Right Hand Rule]]
* [[Angular Velocity]]
* [[Predicting the Position of a Rotating System]]
* [[Translational Angular Momentum]]
* [[The Angular Momentum Principle]]
* [[Angular Momentum of Multiparticle Systems]]
* [[Rotational Angular Momentum]]
* [[Total Angular Momentum]]
* [[Gyroscopes]]
* [[Angular Momentum Compared to Linear Momentum]]

</div>
</div>

<div class="toccolours mw-collapsible mw-collapsed">

===Energy===
<div class="mw-collapsible-content">
*[[The Photoelectric Effect]]
*[[Photons]]
*[[The Energy Principle]]
*[[Predicting Change]]
*[[Rest Mass Energy]]
*[[Kinetic Energy]]
*[[Potential Energy]]
**[[Potential Energy for a Magnetic Dipole]]
**[[Potential Energy of a Multiparticle System]]
*[[Work]]
**[[Work Done By A Nonconstant Force]]
*[[Work and Energy for an Extended System]]
*[[Thermal Energy]]
*[[Conservation of Energy]]
*[[Electric Potential]]
*[[Energy Transfer due to a Temperature Difference]]
*[[Gravitational Potential Energy]]
*[[Point Particle Systems]]
*[[Real Systems]]
*[[Spring Potential Energy]]
**[[Ball and Spring Model]]
*[[Internal Energy]]
**[[Potential Energy of a Pair of Neutral Atoms]]
*[[Translational, Rotational and Vibrational Energy]]
*[[Franck-Hertz Experiment]]
*[[Power (Mechanical)]]
*[[Transformation of Energy]]

*[[Energy Graphs]]
**[[Energy graphs and the Bohr model]]
*[[Air Resistance]]
*[[Electronic Energy Levels]]
*[[Second Law of Thermodynamics and Entropy]]
*[[Specific Heat Capacity]]
*[[The Maxwell-Boltzmann Distribution]]
*[[Electronic Energy Levels and Photons]]
*[[Energy Density]]
*[[Bohr Model]]
*[[Quantized energy levels]]
**[[Spontaneous Photon Emission]]
*[[Path Independence of Electric Potential]]
*[[Energy in a Circuit]]
</div>
</div>

<div class="toccolours mw-collapsible mw-collapsed">

===Collisions===
<div class="mw-collapsible-content">

*[[Collisions]]
Collisions are events that happen very frequently in our day-to-day world. In the realm of Physics, a collision is defined as any sort of process in which before and after a short time interval there is little interaction, but during that short time interval there are large interactions. When looking at collisions, it is first important to understand two very important principles: the Momentum Principle and the Energy Principle. Both principles serve use when talking of collisions because they provide a way in which to analyze these collisions. Collisions themselves can be categorized into 3 main different types: elastic collisions, inelastic collisions, maximally inelastic collisions. All 3 collisions will get touched on in more detail further on.

*[[Elastic Collisions]]
A collision is deemed "elastic" when the internal energy of the objects in the system does not change (in other words, change in internal energy equals 0). Because in an elastic collision no kinetic energy is converted over to internal energy, in any elastic collision Kfinal always equals Kinitial.

*[[Inelastic Collisions]]
A collision is said to be "inelastic" when it is not elastic; therefore, an inelastic collision is an interaction in which some change in internal energy occurs between the colliding objects (in other words, change in internal energy does not equal 0). Examples of such changes that occur between colliding objects include, but are not limited to, things like they get hot, or they vibrate/rotate, or they deform. Because some of the kinetic energy is converted to internal energy during an inelastic collision, Kfinal does not equal Kinitial.
There are a few characteristics that one can search for when identifying inelasticity. These indications include things such as:
*Objects stick together after the collision
*An object is in an excited state after the collision
*An object becomes deformed after the collision
*The objects become hotter after the collision
*There exists more vibration or rotation after the collision

*[[Maximally Inelastic Collision]]
Maximally inelastic collisions, also known as "sticking collisions", are the most extreme kinds of inelastic collisions. Just as its secondary name implies, a maximally inelastic collision is one in which the colliding objects stick together creating maximum dissipation. This does not automatically mean that the colliding objects stop dead because the law of conservation of momentum. In a maximally inelastic collision, the remaining kinetic energy is present only because total momentum can't change and must be conserved.

*[[Head-on Collision of Equal Masses]]
The easiest way to understand this phenomenon is to look at it through an example. In this case, we can analyze it through the common game of billiards. Taking the two, equally massed billiard balls as the system, we can neglect the small frictional force exerted on the balls by the billiard table. The Momentum Principle states that in this head-on collision of billiard balls the total final momentum in the x direction must equal the total initial momentum. However, this alone does not give us the knowledge to know how the momentum will be divided up between the two balls. Considering the law of conservation of energy, we can more accurately depict what will happen. This will also allow for one to identify what kind of collision occurs (elastic, inelastic, or maximally inelastic). It is important to know that head-on collisions of equal masses do not have a definite type of collision associated with it.

*[[Head-on Collision of Unequal Masses]]
Just as with head-on collisions of equal masses, it is easy to understand head-on collisions of unequal masses by viewing it through an example. Let's take for example two balls of unequal masses like a ping-pong ball and a bowling ball. For the purpose of this example (so as to allow for no friction and no other significant external forces), let's imagine these objects collide in outer space inside an orbiting spacecraft. If there were to be a collision between the two, what would one expect to happen? One could expect to see the ping-pong ball collide with the bowling ball and bounce straight back with a very small change of speed. What one might not expect as much is that the bowling ball also moves, just very slowly. Again, this can all be explained through the conservation of momentum and the conservation of energy.

*[[Frame of Reference]]
In the world of Physics, a frame of reference is the perspective from which a system is observed. It can be stationary or sometimes it can even be moving at a constant velocity. In some rare cases, the frame of reference moves at an nonconstant velocity and is deemed "noninertial" meaning the basic laws of physics do not apply. Continuing with the trend of examples, pretend you are at a train station observing trains as they pass by. From your stationary frame of reference, you observe that the passenger on the train is moving at the same velocity as the train. However, from a moving frame of reference, say from the eyes of the train conductor, he would view the train passengers as "anchored" to the train.

*[[Scattering: Collisions in 2D and 3D]]

*[[Rutherford Experiment and Atomic Collisions]]

*[[Coefficient of Restitution]]

*[[testing123]]

</div>
</div>

<div class="toccolours mw-collapsible mw-collapsed">

===Fields===
<div class="mw-collapsible-content">
* [[Electric Field]] of a
** [[Point Charge]]
** [[Electric Dipole]]
** [[Capacitor]]
** [[Charged Rod]]
** [[Charged Ring]]
** [[Charged Disk]]
** [[Charged Spherical Shell]]
** [[Charged Cylinder]]
**[[A Solid Sphere Charged Throughout Its Volume]]
*[[Charge Density]]
*[[Superposition Principle]]
*[[Electric Potential]]
**[[Potential Difference Path Independence]]
**[[Potential Difference in a Uniform Field]]
**[[Potential Difference of point charge in a non-Uniform Field]]
**[[Potential Difference at One Location]]
**[[Sign of Potential Difference]]
**[[Potential Difference in an Insulator]]
**[[Energy Density and Electric Field]]
** [[Systems of Charged Objects]]
*[[Electric Force]]
*[[Polarization]]
**[[Polarization of an Atom]]
*[[Charge Motion in Metals]]
*[[Charge Transfer]]
*[[Magnetic Field]]
**[[Right-Hand Rule]]
**[[Direction of Magnetic Field]]
**[[Magnetic Field of a Long Straight Wire]]
**[[Magnetic Field of a Loop]]
**[[Magnetic Field of a Solenoid]]
**[[Bar Magnet]]
**[[Magnetic Dipole Moment]]
***[[Stern-Gerlach Experiment]]
**[[Magnetic Torque]]
**[[Magnetic Force]]
**[[Earth's Magnetic Field]]
**[[Atomic Structure of Magnets]]
*[[Combining Electric and Magnetic Forces]]
**[[Hall Effect]]
**[[Lorentz Force]]
**[[Biot-Savart Law]]
**[[Biot-Savart Law for Currents]]
**[[Integration Techniques for Magnetic Field]]
**[[Sparks in Air]]
**[[Motional Emf]]
**[[Detecting a Magnetic Field]]
**[[Moving Point Charge]]
**[[Non-Coulomb Electric Field]]
**[[Motors and Generators]]
**[[Solenoid Applications]]
</div>
</div>

<div class="toccolours mw-collapsible mw-collapsed">

===Simple Circuits===
<div class="mw-collapsible-content">
*[[Components]]
*[[Steady State]]
*[[Non Steady State]]
*[[Charging and Discharging a Capacitor]]
*[[Work and Power In A Circuit]]
*[[Thin and Thick Wires]]
*[[Node Rule]]
*[[Loop Rule]]
*[[Resistivity]]
*[[Power in a circuit]]
*[[Ammeters,Voltmeters,Ohmmeters]]
*[[Current]]
**[[AC]]
*[[Ohm's Law]]
*[[Series Circuits]]
*[[Parallel Circuits]]
*[[RC]]
*[[AC vs DC]]
*[[Charge in a RC Circuit]]
*[[Current in a RC circuit]]
*[[Circular Loop of Wire]]
*[[Current in a RL Circuit]]
*[[RL Circuit]]
*[[Feedback]]
*[[Transformers (Circuits)]]
*[[Resistors and Conductivity]]
*[[Semiconductor Devices]]
*[[Insulators]]
*[[Voltage]]
</div>
</div>

<div class="toccolours mw-collapsible mw-collapsed">

===Maxwell's Equations===
<div class="mw-collapsible-content">
*[[Gauss's Flux Theorem]]
**[[Electric Fields]]
***[[Examples of Flux Through Surfaces and Objects]]
**[[Magnetic Fields]]
**[[Proof of Gauss's Law]]
*[[Ampere's Law]]
**[[Magnetic Field of Coaxial Cable Using Ampere's Law]]
**[[Magnetic Field of a Long Thick Wire Using Ampere's Law]]
**[[Magnetic Field of a Toroid Using Ampere's Law]]
*[[Faraday's Law]]
**[[Curly Electric Fields]]
**[[Inductance]]
***[[Transformers (Physics)]]
***[[Energy Density]]
**[[Lenz's Law]]
***[[Lenz Effect and the Jumping Ring]]
**[[Lenz's Rule]]
**[[Motional Emf using Faraday's Law]]
*[[Ampere-Maxwell Law]]
*[[Superconductors]]
**[[Meissner effect]]
</div>
</div>

<div class="toccolours mw-collapsible mw-collapsed">

===Radiation===
<div class="mw-collapsible-content">
*[[Producing a Radiative Electric Field]]
*[[Sinusoidal Electromagnetic Radiaton]]
*[[Lenses]]
*[[Energy and Momentum Analysis in Radiation]]
**[[Poynting Vector]]
*[[Electromagnetic Propagation]]
**[[Wavelength and Frequency]]
*[[Snell's Law]]
*[[Effects of Radiation on Matter]]
*[[Light Propagation Through a Medium]]
*[[Light Scaterring: Why is the Sky Blue]]
*[[Light Refraction: Bending of light]]
*[[Cherenkov Radiation]]
*[[Rayleigh Effect]]
</div>
</div>
<div class="toccolours mw-collapsible mw-collapsed">

===Sound===
<div class="mw-collapsible-content">
*[[Doppler Effect]]
*[[Nature, Behavior, and Properties of Sound]]
*[[Speed of Sound]]
*[[Resonance]]
*[[Sound Barrier]]
</div>
</div>
<div class="toccolours mw-collapsible mw-collapsed">

===Waves===
<div class="mw-collapsible-content">
*[[Bragg's Law]]
*[[Multisource Interference: Diffraction]]
*[[Standing waves]]
*[[Gravitational waves]]
*[[Plasma waves]]
*[[Wave-Particle Duality]]
*[[Electromagnetic Spectrum]]
*[[Color Light Wave]]
*[[The Wave Equation]]
*[[Pendulum Motion]]
*[[Transverse and Longitudinal Waves]]
*[[Planck's Relation]]
*[[interference]]
*[[Polarization of Waves]]
</div>
</div>
<div class="toccolours mw-collapsible mw-collapsed">

===Real Life Applications of Electromagnetic Principles===
<div class="mw-collapsible-content">
*[[Electromagnetic Junkyard Cranes]]
*[[Maglev Trains]]
*[[Spark Plugs]]
*[[Metal Detectors]]
*[[Speakers]]
*[[Radios]]
*[[Ampullae of Lorenzini]]
*[[Electrocytes]]
*[[Generator]]
*[[Measuring Water Level]]
*[[Cyclotron]]
*[[Railgun]]
*[[Magnetic Resonance Imaging]]
*[[Electric Eels]]
*[[Lightning]]

</div>
</div>

<div class="toccolours mw-collapsible mw-collapsed">

===Optics===
<div class="mw-collapsible-content">
*[[Mirrors]]
*[[Refraction]]
*[[Quantum Properties of Light]]
*[[Lasers]]

</div>
</div>

== Resources ==
* Commonly used wiki commands [https://en.wikipedia.org/wiki/Help:Cheatsheet Wiki Cheatsheet]
* A guide to representing equations in math mode [https://en.wikipedia.org/wiki/Help:Displaying_a_formula Wiki Math Mode]
* A page to keep track of all the physics [[Constants]]
* A page for review of [[Vectors]] and vector operations

File:Speedofsound.jpg

2015-12-03T01:24:07Z

Dpatel322:

Main Page

2015-12-01T15:02:48Z

Dpatel322: /* Contact Interactions */