# Talk:Doppler effect

## Speed / velocity

Perhaps I am being pedantic here but I have noted that there seems to be some inconsistence in the article as to referencing v as speed and velocity. As it is scalar, should this not really be referred to speed? I realize this is a minor concern. Agaudin 22:23, 7 November 2006 (UTC)

I don't think so. My physics textbook has a similiar treatment and uses the term "velocity". Since v is signed, it can't be treated as speed (magnitude of velocity). The direction isn't unspecified; it's assumed to be along a line joining the source and observer. Pfalstad 00:24, 13 November 2006 (UTC)

## Relativistic treatment

Is the consensus still for placing the description of the relativistic treatment in its own article or should it be pulled back here? By the way, sorry for omitting the minor change flag on some of my recent updates. -- Alan Peakall 18:42 Dec 6, 2002 (UTC)

## Doppler did not test his hypothesis (?)

According to Alec Eden: The Search for Christian Doppler. Springer Verlag 1992. Doppler didn't test his hypothesis, neither did he base it on observations. However, I am not quite comfortable with writing english, so I would not like to make alterations in the article totally on my own. Could anyone be ready to correct my grammar and spelliong?

Well, according to "Asimov's Biographical Encyclopedia of Science and Technology" (1972 edition, Pan), Doppler is supposed to have spent two days in Holland with a flatbed carriage being pulled back and forth along a railway track, with trumpeters on the carriage playing various notes, and observers with perfect pitch by the track jotting down he actual notes that they heard. It could be a myth, of course, but it sounds like a rather elaborate thing to make up. Unfortunately, that book doesn't provide any further trackable references. ErkDemon 22:06, 30 October 2006 (UTC)
At this time (February 1845) Doppler lived in Prague with his family. The source above states that it was Christoph Hendrik Diederik Buys Ballot that performed the experiment. --Ekko 11:13, 8 November 2006 (UTC)
Okey-doke. Asimov's "biog" encyclopedia is rather lacking in detail, so your (more specific) book sounds like the more reliable source. ErkDemon 11:38, 16 January 2007 (UTC)
Fine, but an actual citation of Buys Ballot's original paper i.e. Buys Ballot(1845), would defo help. No-one seems to cite it at all. Does anyone know if this could be it? Fizeau(1848) seems to suffer the same problem.5.151.82.25 (talk) 08:04, 3 November 2012 (UTC)
Sure, that is the paper in which Buys provided the verification. Ceinturion (talk) 11:39, 3 November 2012 (UTC)

## Not sure one of the formulas is correct

A similar analysis for a moving observer and a stationary source yields the observed frequency...

am I wrong, or does this formula seem incorrect... it would seem if one's speed equals the speed of the wave through the medium, the perceived wavelength should be infinite, and frequency should be zero. This is not what the equation suggests.

It's okay, the quoted velocities are recession velocities. In the "moving-observer" formula, 1- (v0/v) can be rewritten to be more consistent with the format of the previous equation, as (v-v0) /v, which makes it more obvious that when v0=v (moving observer receding from a stationary source at the speed of sound), the predicted frequency does indeed drop to zero. Unfortunately textbook writers seem to quote the various Doppler equations and variants directly from previous books (probably to avoid awful typos), so the formats used can be rather inconsistent and seem to be based more on tradition than mathematical efficiency or consistency. Sometimes the usage of terms in the equations isn't compatible with the accompanying text, so sometimes even the "pros" can end up messing these things up. ErkDemon 22:30, 30 October 2006 (UTC)

## Time Dependence?

I just learned about the doppler effect in my high school physics class, but it seems to me that if the source or observer are not colinear in their motion (they never pass through each other) then the percieved frequency would be related to the cosine of the angle between the motion and the line between the observer and the source. Specifically could the percieved frequency by something like: fa=(c-v*cos(A))fo/c where fa is the apparent frequency, c is the speed in a medium, A is the angle, and fo is the original frequency Also, couldnt you express the cos(A) between the direction of the motion and the line between the observer and the source as: x/(y^2+x^2)^1/2 since the cosine is adjacent (the "x" var) over the hypotenuse. Lastly, x, which is the distance along the line of motion, will be determined by time and velocity. So it seems that:

fa=[c-v*(v*t)/[y^2+(v*t)^2]^1/2]fo/c

for a stationary observer displaced by "y" from the net motion at time t (unfortunately i can't quite think of what t(0) would be)

## Doppler effect / red shift

I notice that there is a comment about red shift not being a result of doppler effect. I am not sure that is true, and it does seem to be in some dispute, especially considering the wikipedia article lists it specifically as a doppler effect measurement. Even if it is true that there is a subtle difference in that implementation, that is information that belongs on the red shift page and/or discussion. I do not think it belongs in this article. If there are no objections, I will remove that paragraph.

Yes, remove it. I think the sentence is accurate but misleading. According to the redshift article, there are several sources of redshift, not just the doppler effect. Pfalstad 20:57, 30 June 2006 (UTC)

## Combined formula

There's a really neat combination of the two formulas in the german WP, so I'm going to paste it here and see if anyone else thinks that it should be included:
${\displaystyle {\frac {f'}{f}}={\frac {c\pm v_{\rm {D}}}{c\mp v_{\rm {S}}}}}$
${\displaystyle v_{\rm {D}}}$ is the velocity of the observer and ${\displaystyle v_{\rm {S}}}$ that of the source. The operators on top are used when they are moving towards and the ones below when they're moving away from each other. —Preceding unsigned comment added by Merctio (talkcontribs)

That's quite cool! :) I'd not seen the "minusplus" symbol before, only the "plusminus". Very useful to be able to use both together in this context! Mucho efficient. Elegant, too, it makes for a nice "reflection" image. Award a point to the German-language Wikians! :) ErkDemon 03:00, 11 June 2007 (UTC)

## Doppler Techniques for geodetic purposes

In my research on Satellite Geodesy, I have found that Doppler techniques have been used extensively as a method of satellite orbit determination. The basic concept being that satellites transmit on a stable frequency, so by measuring the frequency shift, one could derive velocity changes and other orbital parameters. One book that I have found that has a lot of information about this technique is:

Seeber, G. (2003). Satellite Geodesy (2nd ed.). Berlin, Germany: Walter de Gruyter

A limited preview of this book is available on Google Books (see page 181 if it does not take you there automatically) here. I thought that this reference might provide some useful information on this topic as it relates to astronomy and geodesy. ChrisTracy (talk) 23:32, 9 December 2007 (UTC)

## Vandalism

Would it make sense to ask for semi-proection of this page? It appears to be a popular target for vandalism. Retoo (talk) 14:55, 2 March 2008 (UTC)

## Hypnotic illustration

Does anyone else find the illustration near the lead/toc difficult to look at, or even look indirectly at? It may be just that I am tired, but it seemed to spark quite a lot of lateral inhibition which can, of course, be pretty cool if thats what you're looking for. Possibly though considering we are reading text beside it, Image:Velocity0 70c.jpg might be nicer on the eyes and would be able to illustrate the same information? Any thoughts? aliasd·U·T 19:36, 9 May 2008 (UTC)

I find the existing image perfectly suitable for this article, especially as it could stand in for normally experienced forms of doppler effect. The image you suggest, with its pictured velocity of 70% light speed, isn't going to reverberate as clearly with most readers. I say leave the lead/toc image in place, and add the other one elsewhere in the article. Binksternet (talk) 20:24, 9 May 2008 (UTC)

## Monotonic decrease

I have reverted two edits that replaced "monotonic decrease" with "monotonic increase" of the observed frequency as the source moves along a given trajectory. If you think about it, the monotonic decrease is correct (monotonic increase would mean a higher frequency after the source has passed the observer, which is obviously false). Sure, as long as the source is approaching, the observed frequency is higher than the source frequency, but it is decreasing (unless the source is on a collision course with the observer). --Blennow (talk) 14:15, 7 November 2008 (UTC)

The doppler effect in a medium depends on the RELATIVE velocity of the source and the medium AT THE TIME OF EMISSION, and also the RADIAL velocity of the observer and the wavefront normal AT THE TIME OF ABSORPTION.

The doppler effect for light depends on the RADIAL (not relative) velocity of the source AT THE TIME OF EMISSION, and the RADIAL velocity of the observer AT THE TIME OF ABSORPTION.

(This is demonstrated by the annual variance of the doppler shift of the stars due to the earth's changing radial velocity.

(relative velocity = radial velocity + transverse velocity)

Due to propagation delays, the emitted frequency doesn't equal the absorbed frequency until some time AFTER the source has passed.

"Emitted frequency doesn't equal the absorbed frequency..."? Totally depends on relative motion (or lack of motion) of each party. Binksternet (talk) 01:02, 18 July 2009 (UTC)
Amen brother, I'm all over it. One correction, the relativistic doppler effect does actually depend on the transverse velocity. Although things get real hairy when you try to calculate the light time, length contraction, Terrell rotation, relative simultaneity, time dilation, aberration, and doppler effects all at once. It's not always clear when the two objects were transverse to each other. Great point about the annual radial Doppler effect. The annual change in the Doppler shift depends on the observer's radial velocity relative to the light itself. Indeed, the earth hadn't even formed when some of the starlight we see was emitted. Some of the light we see was enjoying its ontological status at a time when neither the source or observer existed. NOrbeck (talk) 06:59, 25 July 2010 (UTC)

## Pictures

I found the two images on the Simple English Wikipedia in the article of the same name to be much easier to understand than for the instance the one on the top right of this article. The images I'm referring to are Doppler_effect_diagrammatic.svg[1] and Dopplerfrequenz.gif[2], both which are found on Wikimedia Commons. Doppler_effect_diagrammatic.png[3] may also be a good one. All three images can be found on Wikimedia Commons and are therefore, as far as I know (I'm new) allowed to be used on this article. I believe these images would make the effect clearer to people that are not very familiar with physics and thus may have a harder time understanding the text. Woodcutterty (talk) 15:10, 28 November 2009 (UTC)

I agree. Let's give it a try. Ceinturion (talk) 15:02, 29 November 2009 (UTC)
Change of wavelength caused by motion the source

It turns out that thumbnailing animated GIFs is not fully supported (Wikipedia:Extended image syntax#Type). Compare the two versions at the right. Users of Internet Explorer (IE8) may notice a background artifact in the thumbnail version. This artifact does not appear in Firefox. To avoid it I am going to use the non-thumbnail version in the article. The disadvantage is that a non-thumbnail image cannot be resized. Ceinturion (talk) 16:17, 29 November 2009 (UTC)

The artifact persists in IE9 for any zoomfactor larger or smaller than 100%. Only in IE, not in other browsers. Ceinturion (talk) 17:39, 5 December 2012 (UTC)

This doesn't seem right, esp. the proximity fuze bit. Doppler is widely used in weather radar and I believe aircraft radar and air traffic control radar as it allows much better discrimination between moving / non moving objects.

It sounds as if the editor hasn't read/doesn't understand the Doppler effect article.I can see what they mean, but it's hard to understand in this form. It is not necessarily or only used to "measure the velocity". Its main feature is it can detect moving objects while ignoring objects that are stationary ie Trees and parked vehicles. Too much emphasis on the "Distance" aspect.

New text in BOLD, Removed text crossed out

"The Doppler effect is used in some applicationstypes of radar, to measure the velocity of detected objects. A radar beam is fired at a moving target — e.g. a motor car, as police use radar to detect speeding motorists — as it approaches or recedes from the radar source. Each successive radar wave has to travel farther to reach the car, before being reflected and re-detected near the source. As each wave has to move farther, the gap between each reflected wave increases, decreasing the frequency. In some situations, If the radar beam is fired at the moving car as it approaches, in which case each successive reflected wave travels a lesser distance, increasing the frequency. In either situation, calculations from the Doppler effect based on the frequency/wavelength change accurately determine the cars' velocity.

Moreover, the proximity fuze, developed during World War II, relies upon Doppler radar[fact] to explode at the correct time, height, distance, etc.[citation needed]

Other applications are weather radar, air traffic control radar, terrain following radars for low-flying military aircraft ie. F-111, B1-B, in fact any application where it is helpful to detect moving objects, not just a raw reflection irrespective of relative motion, eg. A doppler radar will ignore immobile/slow ground reflections (mountains, buildings, slow vehicles), ensuring that this 'ground clutter' does not get mistaken for fast moving passenger aircraft.[citation needed]"

Do laser speed 'traps' use doppler effect at all.? Or just make several distance measurements, and then calculate distance travelled between measurements vs time to get speed? Doppler should stop them measuring a road-side tree at 100 Kph for example.
--220.101.28.25 (talk) 23:06, 5 December 2009 (UTC)

## Subsonic?!

In classical physics (waves in a medium), where the source and the receiver velocities are not supersonic, the relationship between observed frequency f and emitted frequency f0 is given by:

and goes on with the non-relativistic equation (emphasis mine above). Does that really mean the equation is not accurate at Mach 2? Why? Either that's a mistake, or the article should clarify the matter. I don't know which one it is, that's why I'm not fixing it myself. --Gutza T T+ 23:25, 27 February 2010 (UTC)

Doppler effect, in general, happens for the wave at all speed (including the speed that near the speed of light). Classical treatment for Doppler Effect may take sound wave for example. Using sound wave for example, the classical treatment is only valid if the observer and source are both slower than the speed of sound relative to the medium. Speed of emitted wave relative to the medium is regardless of the state of motion of the source. Gutza, I think you are right that there is a mistake then. I will correct it. Thanks for pointing it out. Thljcl (talk) 20:46, 20 March 2010 (UTC)

## Confusing digressions on increase and decrease

Hunter33, I reverted your edit, as the original was correct.[4] On the other hand, although correct, that section is confusing instead of lucid to many readers. Probably it would be better to remove the lines "The above formula assumes that the source is either directly approaching or receding from the observer. If the source approaches the observer at an angle (but still with a constant velocity), the observed frequency that is first heard is higher than the object's emitted frequency. Thereafter, there is a monotonic increase in the observed frequency as it gets closer to the observer, through equality when it is closest to the observer, and a continued monotonic decrease as it recedes from the observer." Actually I think that applies to the digression "A common misconception" as well. Ceinturion (talk) 09:39, 10 May 2010 (UTC)

## Alternative formula with plusminus symbols

About ${\displaystyle f=\left({\frac {v+v_{r}}{v+v_{s}}}\right)f_{0}\,}$: should not the following formula be better f=f'(v+-vr)/(v-+vs) (134.184.100.155 (talk) 03:48, 9 June 2010 (UTC))

Do you mean replacing the current formula ${\displaystyle f=\left({\frac {v+v_{r}}{v+v_{s}}}\right)f_{0}\,}$ by an alternative formula ${\displaystyle f'=f\left({\frac {v\pm v_{\rm {r}}}{v\mp v_{\rm {s}}}}\right)}$, similar to a previous suggestion on this Talk-page?[5]. Please use LaTeX for editing formulas, that is easier to read. Ceinturion (talk) 07:16, 9 June 2010 (UTC)
Yes replacing it by ${\displaystyle f'=f\left({\frac {v\pm v_{\rm {r}}}{v\pm v_{\rm {s}}}}\right)}$ since there are 4 possibilities. The source can move,observer can move and the movement in the opposite direction. They can all be combined in 1 formula.(134.184.100.155 (talk) 20:10, 9 June 2010 (UTC))
So your main concern is using the ${\displaystyle \pm }$ symbol. Christian Doppler himself used that symbol, because in his mind velocity was always a positive number (speed, the magnitude of the velocity vector). However, the ${\displaystyle \pm }$ symbol is mathematically redundant. Velocity is a variable that may be positive or negative. Ceinturion (talk) 23:32, 9 June 2010 (UTC)

While the use the ${\displaystyle \pm }$ and ${\displaystyle \mp }$ symbols may be mathematically redundant, it does aid understanding. My default textbook for all things physics is Resnick, Halliday & Krane Physics, 4th ed vol 1, John Wiley & Sons 1992 that was given to me during my undergraduate degree. It uses the ${\displaystyle \pm }$ and ${\displaystyle \mp }$ symbols. I would argue that their inclusion aids clarity.Graeme.e.smith (talk) 19:41, 10 April 2012 (UTC)

The choice is determined by the definition of v. This wikipedia article defines v as a velocity, which is signed. Hence ${\displaystyle \pm }$ and ${\displaystyle \mp }$ should not be used. In contrast, Resnick defines v as a speed, which is unsigned. Hence ${\displaystyle \pm }$ and ${\displaystyle \mp }$ have to be used. Moretim (talk) 00:21, 16 November 2012 (UTC)

## Direction change

I think the current formula ${\displaystyle f=\left({\frac {v+v_{r}}{v+v_{s}}}\right)f_{0}\,}$ should be written as ${\displaystyle f=\left({\frac {v-v_{r}}{v-v_{s}}}\right)f_{0}\,}$, because ${\displaystyle v\,}$ is the velocity of the wave so that both of ${\displaystyle v_{r}\,}$ and ${\displaystyle v_{s}\,}$ should be on the same line of ${\displaystyle v\,}$, then, when two velocities have same direction, we want the difference of their speeds, when two velocities have different directions, we want the sum of their speeds.Jh17710 (talk) 21:18, 16 January 2011 (UTC)

The second half of each definition for ${\displaystyle v_{r}\,}$ and ${\displaystyle v_{s}\,}$ to define the positive or negative should be removed because the positive and negative are decided by the relative velocity direction of ${\displaystyle v_{r}\,}$ to ${\displaystyle v\,}$ and ${\displaystyle v_{s}\,}$ to ${\displaystyle v\,}$.Jh17710 (talk) 21:06, 16 January 2011 (UTC)
And so that ${\displaystyle v_{s,r}=v_{s}-v_{r}\,}$ should be ${\displaystyle v_{s,r}=v_{r}-v_{s}\,}$Jh17710 (talk) 21:36, 16 January 2011 (UTC)
Note: the formulas are now properly sourced. DVdm (talk) 14:43, 18 January 2011 (UTC)
I agree that the signs in the formula contradict the stated direction of ${\displaystyle v_{r}\,}$ and ${\displaystyle v_{s}\,}$. For instance, if the source is travelling away from the receiver, then the velocity of the wave will be ${\displaystyle c-v_{s}\,}$. Do editors regard this as resolved? It's hard for me to tell.Adefensibleorigin (talk) 20:17, 12 February 2014 (UTC)
If the source is travelling away from the receiver (and the receiver is at rest), ${\displaystyle v_{s}\,}$ is positive and ${\displaystyle f\,}$ is smaller than ${\displaystyle f_{0}\,}$. The velocity of the wave (relative to the medium) is ${\displaystyle c\,}$, independent of ${\displaystyle v_{s}\,}$. Ceinturion (talk) 21:51, 15 February 2014 (UTC)

## Image restored, colours correct

Two days ago 190.134.15.113 removed the image at the right because "Erroneous image concept. Only the spectral lines are shifted, not the colours of the continous background." However, the background represents the colour perception by human observers on earth. It is what we would see using a spectroscope. The background is not about colour perception by humans or aliens living at those distant galaxies. Therefore I restored the image. Ceinturion (talk) 06:28, 24 March 2011 (UTC)

## Wave speed

Wave speed equal to frequency times wavelength is a material property. The first figure, upper part, gives the false impression that wave speed depends on source speed. A better caption could be “Waves seen from a source moving at constant velocity near the wave speed.” (HCPotter (talk) 08:50, 27 November 2011 (UTC))

Removing the offensive figure part is one solution to the problem,

but I believe retaining it with the revised caption would give insight into the Doppler equation origin that the page otherwise lacks. (HCPotter (talk) 13:14, 4 December 2011 (UTC))

## Photon volume

For light a Doppler effect is readily developed from Lorentz time dilatation. Relativistic Doppler effect It gives an expression dependent on the relative velocity component in the direction from observer to source in which direction the light wavelength is presumed to change. For photons with volume proportional to wavelength cubed, however, the photon size will change. For most physical systems in which the source and observer move relative to some reference object, the component transformations are generally not Lorentzian. (HCPotter (talk) 09:56, 11 December 2011 (UTC))

All the four animated pictures in the section "general" have a little blemish: The first ring is slightly more spaced than the following ones. Could this be adjusted?

Thanks. 160.85.33.84 (talk) 10:02, 16 January 2012 (UTC)

## Analysis : "actually the wavelength which is affected". Is this also the case for "moving observer, stationary source" ?

Regd. Analysis section: Does not explicitly mention which case is analysed - I assumed "moving source, stationary observer".

It explains "So it is actually the wavelength which is affected". Ok.

However, in the other case, "moving observer, stationary source", I was confused by the phrase "similar analysis". Analysis may be similar but does the same explanation "actually the wavelength which is affected" hold? In this case, doesn't wavelength "actually" remain same and relative/perceived sound speed change, thus affecting perceived frequency?

In the section "General" is its written:

the relationship between observed frequency f and emitted frequency f0 is given by:

where
${\displaystyle c\;}$ is the velocity of waves in the medium;
${\displaystyle v_{r}\,}$ is the velocity of the receiver relative to the medium; positive if the receiver is moving towards the source;
${\displaystyle v_{s}\,}$ is the velocity of the source relative to the medium; positive if the source is moving away from the receiver.

If I assume that c is meant to be always positive (is that the case here?) and for example the receiver to be at rest and the sender moving in the direction of the receiver with ${\displaystyle |v_{s}|={\frac {1}{2}}c}$ I get:
${\displaystyle f=\left({\frac {c}{c-(-{\frac {1}{2}}c)}}\right)f_{0}={\frac {1}{1.5}}f_{0}}$
which means the frequency gets lower, which is wrong. I think correct would be:

${\displaystyle v_{s}\,}$ is the velocity of the source relative to the medium; positive if the source is moving towards the receiver. Manuel Walter (talk) 19 March 2012
Somebody fixed it today by changing the formula: ${\displaystyle f=\left({\frac {c+v_{r}}{c+v_{s}}}\right)f_{0}\,}$, instead of the definition of ${\displaystyle v_{s}\,}$. An advantage of this fix is that it is compatible with a definition in the same paragraph ( ${\displaystyle v_{s,r}=v_{s}-v_{r}\,}$ ), and formulas in the next paragraph. Ceinturion (talk) 20:40, 21 March 2012 (UTC)

The article states that the wavelength is altered. This is not true. It is the timing difference between pulses that reveals how fast an object is moving and in which direction. — Preceding unsigned comment added by 78.146.91.223 (talk) 10:21, 3 June 2012 (UTC)

## Remove "a common misconception"?

Shouldn't we remove the somewhat nonsensical paragraph "a common misconception"? It says: "Craig Bohren pointed out in 1991 that some physics textbooks erroneously state that the observed frequency increases as the object approaches an observer and then decreases only as the object passes the observer. ... Bohren proposed that this common misconception might occur because the intensity of the sound increases as an object approaches an observer and decreases once it passes and recedes from the observer and that this change in intensity is misperceived as a change in frequency." I have no access to Bohren's article, but if he really said so he was probably not serious. It is very unlikely that authors of physics books fail to understand the difference between frequency and intensity. The Doppler effect is not a difficult concept. More likely it was just sloppy language. Authors on any subject may accidentally (and incorrectly) replace "is increased" by "increases" out of fear for the passive voice. A correct statement would have been: "the observed frequency is increased as the object approaches an observer and then is decreased only as the object passes the observer". There is no common misconception among authors of physics books, it is just sloppy language. Any objections against removal? 1st version of paragraph (2008) Current version Ceinturion (talk) 10:55, 12 September 2012 (UTC)

Nearly two weeks later, and nobody has posted any objections, so I am going to remove the section within a few days. Ceinturion (talk) 22:32, 24 September 2012 (UTC)
Done. Ceinturion (talk) 13:27, 26 September 2012 (UTC)

## Sound examples

This came up at GLAMcamp in London, so here are the sound example from de-wiki. I'm not sure how and where to integrate them into the article, so I'll leave that up to User:Andrew Gray ;-)

Die Tonbeispiele geben die Tonhöhen, die ein ruhender Beobachter hört, wenn eine Signalquelle an ihm vorbeifliegt. Sie vernachlässigen den Effekt, dass die sich entfernende Quelle länger zu hören ist als die sich nähernde:

Frequenz f0 = 400 Hz, relative Geschwindigkeit v/c = 0,1 (dann ist fzu_max = 440 Hz und fweg_min = 360 Hz):
(1) Langsam bewegte Signalquelle, die Beobachter in geringem Abstand passiert.
(2) : wie (1), aber Passieren der Signalquelle in größerem Abstand.
(3) : wie (2), Abstand noch größer.

Erhöht sich die relative Geschwindigkeit, verschieben sich die Frequenzen:

Frequenz wie oben, aber v/c = 0,42 (dann ist fzu_max = 690 Hz, fweg_min = 280 Hz).
(4) : Abstand wie (2).

--Cirdan (talk) 10:44, 16 September 2012 (UTC)

## Sign conventions

The signs in the text are inconsistent with the signs in the image legends. Before choosing, let's see which conventions are used in different physics books.

• Single coordinate system for s and r, 1 dimensional
(1) ${\displaystyle f=\left({\frac {c+v_{r}}{c+v_{s}}}\right)f_{0}\,}$, positive direction for ${\displaystyle v_{r}\,}$ and ${\displaystyle v_{s}\,}$ is from receiver towards source. Used by Sears&Zemansky University Physics.
(2) ${\displaystyle f=\left({\frac {c-v_{r}}{c-v_{s}}}\right)f_{0}\,}$, positive direction for ${\displaystyle v_{r}\,}$ and ${\displaystyle v_{s}\,}$ is from source towards receiver. Used by Alonso&Finn Physics.
• Dual coordinate system for s and r (mirrored), 1 dimensional
(3) ${\displaystyle f=\left({\frac {c+v_{r}}{c-v_{s}}}\right)f_{0}\,}$, positive direction for ${\displaystyle v_{r}\,}$ and ${\displaystyle v_{s}\,}$ is towards each other. Used by Serway Physics for Scientists and Engineers.
(4) ${\displaystyle f=\left({\frac {c-v_{r}}{c+v_{s}}}\right)f_{0}\,}$, positive direction for ${\displaystyle v_{r}\,}$ and ${\displaystyle v_{s}\,}$ is away from each other. Used by nobody.
(5) ${\displaystyle f=\left({\frac {c\pm v_{\rm {r}}}{c\mp v_{\rm {s}}}}\right)f_{0}\,}$, is the combination of the above formulas, where ${\displaystyle v_{r}\,}$ and ${\displaystyle v_{s}\,}$ are (non-negative) speeds instead of velocities (which may be negative). Used by Halliday&Resnick Physics, Giancoli Physics, Gupta Engineering Physics, Doppler himself.
• Vector form without specific coordinate system, 3 dimensional
(6) ${\displaystyle f=\left({\frac {c-{\vec {v}}_{r}\cdot {\vec {e}}_{sr}}{c-{\vec {v}}_{s}\cdot {\vec {e}}_{sr}}}\right)f_{0}\,}$, where ${\displaystyle {\vec {e}}_{sr}}$ is a unit vector.

The single coordinate systems are theoretically more fundamental, the dual coordinate systems might be more convenient in some practical problems. Ceinturion (talk) 01:40, 14 December 2012 (UTC)

Solved inconsistency: replaced variables by values in the image legends, without altering the formulas in the text. Ceinturion (talk) 00:39, 16 December 2012 (UTC)

## Animated gif speed browser dependent?

Strange: the speed of some of the animated gifs in the article is browser dependent. In Google Chrome the red dot in the left animation moves to the right in 1 second, but it is slowed down to 3 seconds in Internet Explorer (IE9). In contrast, The speed of the animated gif at the right is browser independent. Why is that? Ceinturion (talk) 00:32, 18 December 2012 (UTC)

Ah, explanation found: IE has a minimum frame delay of 0.06 s; anything below that is rounded up to 0.10 s. GC has a minimum frame delay of 0.02 s; anything below that is rounded up to 0.10 s. The left animation has a frame delay of 0.03 s, so it is slowed down by IE. The right animation has a frame delay of 0.10s, so it is not slowed down by IE. Ceinturion (talk) 01:04, 18 December 2012 (UTC)
I noticed that the new browser version IE10 displays the left animation correctly, at the same speed as GC. Apparently Microsoft has solved this issue. Ceinturion (talk) 20:18, 6 April 2013 (UTC)

## Rayleigh's backwards music effect "in front of" or "behind"?

Today and last month there were contradictory edits concerning Rayleigh's backwards music effect occuring "in front of" or "behind" the source.[6] [7] Actually it should be correlated to before and after: "Music emitted when the observer was in front of the source, will be heard backwards, when the source is behind the observer." To avoid the confusion, we would better not mention the location, just like Rayleigh did. Ceinturion (talk) 22:03, 15 February 2013 (UTC)

## Airplanes

Mention the sudden onset, then gradual decrease, of the sound (intensity, not frequency) of a passing airplane, is merely due to the front of an airplane being quieter than the rear, even when on the ground. https://groups.google.com/d/topic/sci.physics.acoustics/vWwNsCZ_gwk/discussion Jidanni (talk) 21:16, 7 December 2013 (UTC)

## Scientific inaccurate portrayal of Doppler effect

The gif animation used to demonstrate the pitch change of a moving vehicle seemed wrong to me.

Doppler effect

In the animation, the wave travel forth travels at a faster speed and the wave travel backward travels slower after the car starts moving, which is not true. Unless the wave travel through different medium with different density, the speed that wave travels remains the same. Qranger1980 (talk) 02:59, 4 March 2014 (UTC)AA

I don't see your problem on my computer. In the animation only the wavelength changes, not the speed. When the car starts to move, short waves appear in front of the car. The crests of these short waves move at the same speed as the earlier emitted standard waves. Ceinturion (talk) 12:00, 5 March 2014 (UTC)