Relativistic Doppler Effect - Revision history

Dsharma323: Added difficult question

2024-12-07T17:37:46Z

Added difficult question

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 <math>f_o = 6.0 \times 10^{12} \frac{\sqrt{1 - \frac{.4c}{c}}}{\sqrt{1 + \frac{.4c}{c}}} = 6.0 \times 10^{12} \frac{\sqrt{1 - .4}}{\sqrt{1 + .4}} = 6.0 \times 10^{12} \frac{\sqrt{.6}}{\sqrt{1.4}} = 6.0 \times 10^{12} * 0.6547 = 3.9282 \times 10^{12}</math>
-Thus, the observed frequency is approximately <math>3.9282 \times 10^{12} \text{Hz}</math>.
+Thus, the observed frequency is approximately <math>3.9282 \times 10^{12} \text{Hz}</math>
 ===Difficult===
-<b>Q:</b>
+<b>Q:</b> A spacecraft traveling at <math>v = 0.6c</math> at an angle <math>\theta = 60^\circ</math> relative to the line of sight from an observer on Earth. The spacecraft emits a radio signal (<math>\lambda_s = 2 \text{m}</math>). Calculate the wavelength of the observed light.
 ==Connectedness==

Dsharma323: Add simple, middling question

2024-12-07T17:09:31Z

Add simple, middling question

@@ Line 49: / Line 49: @@
 ==Examples==
 ===Simple===
 ===Middling===
 ===Difficult===
 ==Connectedness==

Dsharma323: Connectedness, History, See Also, References

2024-12-07T11:00:48Z

Connectedness, History, See Also, References

← Older revision		Revision as of 07:00, 7 December 2024
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	In the case with light in a vacuum however, there is no medium of propagation. Instead the effect occurs due to relativistic effects, primarily time dilation, which is described by Einstein's theory of Special Relativity.		In the case with light in a vacuum however, there is no medium of propagation. Instead the effect occurs due to relativistic effects, primarily time dilation, which is described by Einstein's theory of Special Relativity.

	While we experience the classical Doppler effect as a change in a sound's pitch, the ~~eelativistic~~ Doppler effect causes a change in the frequency and wavelength of the light wave. If the light source is moving towards the observer, the light's frequency will increase and wavelength will decrease, causing it to "blueshift". If the light source is moving away from the observer, the light's frequency will decrease and wavelength will increase, causing it to "redshift".		While we experience the classical Doppler effect as a change in a sound's pitch, the relativistic Doppler effect causes a change in the frequency and wavelength of the light wave. If the light source is moving towards the observer, the light's frequency will increase and wavelength will decrease, causing it to "blueshift". If the light source is moving away from the observer, the light's frequency will decrease and wavelength will increase, causing it to "redshift".

	It is important to note that there are other cosmological effects that can cause redshifting and blueshifting of light.		It is important to note that there are other cosmological effects that can cause redshifting and blueshifting of light.
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	==Examples==		==Examples==
	~~Be sure to show all steps in your solution and include diagrams whenever possible~~

	===Simple===		===Simple===

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	==Connectedness==		==Connectedness==
	~~#How~~ is ~~this topic connected~~ to ~~something that you are interested in?~~		By analyzing the redshifts and blueshifts of light from celestial object, it is possible to determine their motion relative to Earth, which can then provide insight into the expansion of the universe, whether a star is really a binary star system, the movement of stars within galaxies, and other cosmological phenomena.
	~~#How~~ is ~~it connected to your major?~~
	~~#Is there an interesting industrial application?~~

	==History==		==History==
	~~Put this idea~~ in ~~historical context~~. ~~Give~~ the ~~reader~~ the ~~Who~~, ~~What~~, ~~When~~, ~~Where~~, ~~and Why~~.		The classical Doppler effect was first proposed in 1842 by Christian Doppler. It was extended into the relativistic Doppler effect with Einstein's theory of special relativity in 1905. In 1938 Ives and Stilwell were the first to prove that the transverse Doppler effect involved time dilation, and that the formula for it was correct, though they did not directly measure the transverse Doppler effect. This became possible later, after the creation of particle accelerator technology, as implemented by Hasselkamp et al. in 1979.

	== See also ==		== See also ==
	~~Are there related topics or categories in this wiki resource for the curious reader to explore? How does this topic fit into that context?~~		* [https://www.physicsbook.gatech.edu/Einstein%27s_Theory_of_Special_Relativity Einstein's Theory of Special Relativity]
			* [https://www.physicsbook.gatech.edu/Time_Dilation Time Dilation]
	~~===Further reading===~~		* [https://www.physicsbook.gatech.edu/Lorentz_Transformations Lorentz Transformations]
	~~Books, Articles or other print media on this topic~~

	===External links===		===External links===
	~~Internet resources on this topic~~		* https://www.youtube.com/watch?v=d6ieu0Z8gAo
			* https://www.youtube.com/watch?v=JJciUSRX74c
			* https://en.wikipedia.org/wiki/Gravitational_redshift
			* https://en.wikipedia.org/wiki/Expansion_of_the_universe
			* https://en.wikipedia.org/wiki/Ives%E2%80%93Stilwell_experiment

	==References==		==References==
	~~This section contains the the references you used while writing this page~~		[1] Relativistic Doppler effect. In <i>Wikipedia<i>. Retrieved from https://en.wikipedia.org/wiki/Relativistic_Doppler_effect

			[2] Ling, S. J., Sanny, J., & Moebs, W. 5.7 Doppler Effect for Light. In <i>University Physics Volume 3</i>. Houston, Texas: OpenStax. Retrieved from https://openstax.org/books/university-physics-volume-3/pages/5-7-doppler-effect-for-light

			[3] Guth, A. Lecture notes 1: The Doppler Effect and Special Relativity. Retrieved https://web.mit.edu/8.286/www/lecn18/ln01-euf18.pdf


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

Dsharma323: Add simplified formulas for transverse/longitudinal cases

2024-12-07T09:42:08Z

Add simplified formulas for transverse/longitudinal cases

← Older revision		Revision as of 05:42, 7 December 2024
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	'''Claimed - Dev Sharma (Fall 2024)''' <br>		'''Claimed - Dev Sharma (Fall 2024)''' <br>
	The ~~Relativistic~~ Doppler ~~Effect~~ describes the wavelength and frequency of light due to relative motion between the source and an observer.		The relativistic Doppler effect describes the wavelength and frequency of light due to relative motion between the source and an observer.

	==The Main Idea==		==The Main Idea==
	The classical Doppler ~~Effect~~ describes the change in frequency of a wave in relation to an observer moving relative to the source of the wave. A common example is the change in pitch of the sound of a passing vehicle -- the noise has a higher pitch when the vehicle is approaching and a lower pitch when it is receding. This occurs due to the compression/stretching of the sound wave relative to the observer as it move through its medium (READ MORE HERE).		The classical Doppler effect describes the change in frequency of a wave in relation to an observer moving relative to the source of the wave. A common example is the change in pitch of the sound of a passing vehicle -- the noise has a higher pitch when the vehicle is approaching and a lower pitch when it is receding. This occurs due to the compression/stretching of the sound wave relative to the observer as it move through its medium (READ MORE HERE).

	In the case with light in a vacuum however, there is no medium of propagation. Instead the effect occurs due to relativistic effects, primarily time dilation, which is described by Einstein's theory of Special Relativity.		In the case with light in a vacuum however, there is no medium of propagation. Instead the effect occurs due to relativistic effects, primarily time dilation, which is described by Einstein's theory of Special Relativity.

	While we experience the classical Doppler ~~Effect~~ as a change in a sound's pitch, the ~~Relativistic~~ Doppler ~~Effect~~ causes a change in the frequency and wavelength of the light wave. If the light source is moving towards the observer, the light's frequency will increase and wavelength will decrease, causing it to "blueshift". If the light source is moving away from the observer, the light's frequency will decrease and wavelength will increase, causing it to "redshift".		While we experience the classical Doppler effect as a change in a sound's pitch, the eelativistic Doppler effect causes a change in the frequency and wavelength of the light wave. If the light source is moving towards the observer, the light's frequency will increase and wavelength will decrease, causing it to "blueshift". If the light source is moving away from the observer, the light's frequency will decrease and wavelength will increase, causing it to "redshift".

	It is important to note that there are other cosmological effects that can cause redshifting and blueshifting of light.		It is important to note that there are other cosmological effects that can cause redshifting and blueshifting of light.
	* Gravitational redshift occurs due to the influence of strong gravitational fields on light (READ MORE HERE).		* Gravitational redshift occurs due to the influence of strong gravitational fields on light (READ MORE HERE).
	* Cosmological redshift is caused by the expansion of the universe "stretching" light over large distances (READ MORE HERE).		* Cosmological redshift is caused by the expansion of the universe "stretching" light over large distances (READ MORE HERE).
	These effects operate through different principles, and so are not covered in any greater detail in this article.		These effects operate through very different principles than the relativistic Doppler effect, and so are not covered in any greater detail in this article.

	===Derivation of General Relativistic Doppler Formula===		===Derivation of General Relativistic Doppler Formula===
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	The frequency of the light wave is the inverse of the period. Thus, if we let <math>f_o = \frac{1}{\Delta t}</math> represent the frequency of the light from the observer's frame of reference and <math>f_s = \frac{1}{\Delta \tau}</math> represent the frequency of the light from the source's reference frame, we have <math>\frac{1}{f_o} = \frac{1}{f_s} \frac{1}{\sqrt{1 - \frac{v^2}{c^2}}} (1 - \frac{v \cos(\theta)}{c})</math>		The frequency of the light wave is the inverse of the period. Thus, if we let <math>f_o = \frac{1}{\Delta t}</math> represent the frequency of the light from the observer's frame of reference and <math>f_s = \frac{1}{\Delta \tau}</math> represent the frequency of the light from the source's reference frame, we have <math>\frac{1}{f_o} = \frac{1}{f_s} \frac{1}{\sqrt{1 - \frac{v^2}{c^2}}} (1 - \frac{v \cos(\theta)}{c})</math>

	We can rewrite this to find the general formula for the ~~Relativistic~~ Doppler ~~Effect~~: <math>f_o = f_s \frac{\sqrt{1 - \frac{v^2}{c^2}}}{1 - \frac{v \cos(\theta)}{c}}</math>		We can rewrite this to find the general formula for the relativistic Doppler effect: <math>f_o = f_s \frac{\sqrt{1 - \frac{v^2}{c^2}}}{1 - \frac{v \cos(\theta)}{c}}</math>

	It is clear to see that <math>f_o \neq f_s</math> and that their relationship depends on both the velocity of the moving light source and the angle at which the source is moving with respect to the line of sight of the observer.		It is clear to see that <math>f_o \neq f_s</math> and that their relationship depends on both the velocity of the moving light source and the angle at which the source is moving with respect to the line of sight of the observer.

	===A Mathematical Model===		===A Mathematical Model===
			We have the general formula for the relativistic Doppler effect: <math>f_o = f_s \frac{\sqrt{1 - \frac{v^2}{c^2}}}{1 - \frac{v \cos(\theta)}{c}}</math>

			We can simplify this formula to consider some common cases of the relativistic Doppler effect: the transverse Doppler effect, and the longitudinal Doppler effect.

			The transverse Doppler effect is when the light source is traveling perpendicular to the observer (i.e. <math>\theta</math> = 90). In this case, the general formula simplifies to <math>f_o = f_s \sqrt{1 - \frac{v^2}{c^2}}</math>

			The longitudinal Doppler effect is when the light source is moving directly towards/away from the observer (i.e. <math>\theta</math> = 0). In the case that the source is traveling directly towards the observer, the general formula simplifies to <math>f_o = f_s \frac{\sqrt{1 + \frac{v}{c}}}{\sqrt{1 - \frac{v}{c}}}</math>. In the case that the traveling directly away from the observer, the general formula simplifies to <math>f_o = f_s \frac{\sqrt{1 - \frac{v}{c}}}{\sqrt{1 + \frac{v}{c}}}</math>

	===A Computational Model===		===A Computational Model===

Dsharma323: Add main idea, derivation of general formula, computational model

2024-12-07T09:29:36Z

Add main idea, derivation of general formula, computational model

← Older revision		Revision as of 05:29, 7 December 2024
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	===Derivation of General Relativistic Doppler Formula===		===Derivation of General Relativistic Doppler Formula===
	Consider a given light source moving at relativistic speed <math>v</math>, and an observer is observing the light at angle <math>\theta</math> relative to the source's motion.		Consider a given light source moving at relativistic speed <math>v</math>, and an observer that is observing the light at angle <math>\theta</math> relative to the source's motion. Assume that the distance between the source and the observer is large enough that <math>\theta</math> does not change any meaningful amount as the source moves.

			The source emits some light at <math>t_1</math>, which is then received by the observer at time <math>t_1^r</math>. After emitting the light, the source keeps moving at velocity <math>v</math> for time <math>\Delta t</math> before emitting more light at time <math>t_2</math>, which is then received by the observer at time <math>t_2^r</math>; at this time the source and observer are distance <math>L</math> away. All of these measurements are measured in the observer reference frame.

			It is trivial to see that <math>t_2^r = t_2 + \frac{L}{c}</math> and that <math>t_1^r = t_1 + \frac{L + v \Delta t \cos(\theta)}{c}</math>

			We can combine these equations to find the change time for the observer between receiving the two signals. <math>t_2^r - t_1^r = (t_2 + \frac{L}{c}) - (t_1 + \frac{L + v \Delta t \cos(\theta)}{c}) = (t_2 - t_1) + (\frac{L}{c} - \frac{L + v \Delta t \cos(\theta)}{c}) = (t_2 - t_1) + (\frac{L - L - v \Delta t \cos(\theta)}{c}) = (t_2 - t_1) - \frac{v \Delta t \cos(\theta)}{c}</math>

			We can now rewrite this as <math>\Delta t^r = \Delta t (1 - \frac{v \cos(\theta)}{c})</math>

			We previously stated that <math>t</math> is from the observer's reference frame. Due to time dilation effects from the light source moving at relativistic speeds, we can use a Lorentz Transformation to find the relationship between the time in the observer's reference frame <math>t</math> and the time in the light source's reference frame <math>\tau</math>, such that <math>t = \frac{\tau}{\sqrt{1 - \frac{v^2}{c^2}}}</math>

			From this, we have that <math>\Delta t^r = \frac{\Delta \tau}{\sqrt{1 - \frac{v^2}{c^2}}} (1 - \frac{v \cos(\theta)}{c})</math>

			The frequency of the light wave is the inverse of the period. Thus, if we let <math>f_o = \frac{1}{\Delta t}</math> represent the frequency of the light from the observer's frame of reference and <math>f_s = \frac{1}{\Delta \tau}</math> represent the frequency of the light from the source's reference frame, we have <math>\frac{1}{f_o} = \frac{1}{f_s} \frac{1}{\sqrt{1 - \frac{v^2}{c^2}}} (1 - \frac{v \cos(\theta)}{c})</math>

			We can rewrite this to find the general formula for the Relativistic Doppler Effect: <math>f_o = f_s \frac{\sqrt{1 - \frac{v^2}{c^2}}}{1 - \frac{v \cos(\theta)}{c}}</math>

			It is clear to see that <math>f_o \neq f_s</math> and that their relationship depends on both the velocity of the moving light source and the angle at which the source is moving with respect to the line of sight of the observer.

	===A Mathematical Model===		===A Mathematical Model===
	What are the mathematical equations that allow us to model this topic. For example <math>{\frac{d\vec{p}}{dt}}_{system} = \vec{F}_{net}</math> where '''p''' is the momentum of the system and '''F''' is the net force from the surroundings.

	===A Computational Model===		===A Computational Model===
	~~How do we visualize or predict using this topic. Consider embedding some vpython code here [~~https://~~trinket~~.io/~~glowscript~~/~~31d0f9ad9e Teach hands-on with GlowScript]~~		This Desmos model represents the Relativistic Doppler Effect: https://www.desmos.com/calculator/9laabrg6qr.

	==Examples==		==Examples==

Dsharma323 at 07:20, 7 December 2024

2024-12-07T07:20:11Z

← Older revision		Revision as of 03:20, 7 December 2024
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	===Derivation of General Relativistic Doppler Formula===		===Derivation of General Relativistic Doppler Formula===
	Consider a given light source moving at relativistic speed <math>v</math>, and an observer is observing the light at angle <math>\theta</math> relative to the source's motion.		Consider a given light source moving at relativistic speed <math>v</math>, and an observer is observing the light at angle <math>\theta</math> relative to the source's motion.





	===A Mathematical Model===		===A Mathematical Model===

Dsharma323 at 04:55, 7 December 2024

2024-12-07T04:55:25Z

@@ Line 1: / Line 1: @@
 '''Claimed - Dev Sharma (Fall 2024)''' <br>
-The Relativistic Doppler Effect describes the alteration of the wavelength and frequency of light (Classical Doppler Effect) while accounting for the consequences of Special Relativity.
+==The Main Idea==
-==Classical Doppler Effect==
+In the case with light in a vacuum however, there is no medium of propagation. Instead the effect occurs due to relativistic effects, primarily time dilation, which is described by Einstein's theory of Special Relativity.
-Consider a police car that is speeding past you with its sirens on. Have you ever noticed that the pitch of the siren is higher as it approaches you, but drops as it diverges from you? The beginning of the audio correlates to the rightmost figure and progresses to the leftmost.

Dsharma323 at 23:27, 6 December 2024

2024-12-06T23:27:56Z

← Older revision		Revision as of 19:27, 6 December 2024
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	(~~Note: This page is actively being eddited~~)		'''Claimed - Dev Sharma (Fall 2024)''' <br>

	The Relativistic Doppler Effect describes the alteration of the wavelength and frequency of light (Classical Doppler Effect) while accounting for the consequences of Special Relativity.		The Relativistic Doppler Effect describes the alteration of the wavelength and frequency of light (Classical Doppler Effect) while accounting for the consequences of Special Relativity.

	==Classical Doppler Effect==		==Classical Doppler Effect==
	Consider a police car that is speeding past you with its sirens on. Have you ever noticed that the pitch of the siren is higher as it approaches you, but drops as it diverges from you? The beginning of the audio correlates to the rightmost figure and progresses to the leftmost.		Consider a police car that is speeding past you with its sirens on. Have you ever noticed that the pitch of the siren is higher as it approaches you, but drops as it diverges from you? The beginning of the audio correlates to the rightmost figure and progresses to the leftmost.

Ecarder: Created page with "(Note: This page is actively being eddited) The Relativistic Doppler Effect describes the alteration of the wavelength and frequency of light (Classical Doppler Effect) while accounting for the consequences of Special Relativity. ==Classical Doppler Effect== Consider a police car that is speeding past you with its sirens on. Have you ever noticed that the pitch of the siren is higher as it approaches you, but drops as it diverges from you? The beginning of the audio cor..."

2022-09-29T03:34:43Z

Created page with "(Note: This page is actively being eddited) The Relativistic Doppler Effect describes the alteration of the wavelength and frequency of light (Classical Doppler Effect) while accounting for the consequences of Special Relativity. ==Classical Doppler Effect== Consider a police car that is speeding past you with its sirens on. Have you ever noticed that the pitch of the siren is higher as it approaches you, but drops as it diverges from you? The beginning of the audio cor..."

New page

(Note: This page is actively being eddited)
The Relativistic Doppler Effect describes the alteration of the wavelength and frequency of light (Classical Doppler Effect) while accounting for the consequences of Special Relativity.

==Classical Doppler Effect==
Consider a police car that is speeding past you with its sirens on. Have you ever noticed that the pitch of the siren is higher as it approaches you, but drops as it diverges from you? The beginning of the audio correlates to the rightmost figure and progresses to the leftmost.