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Natural Science Forum / Physics / Acoustics / February 2004Acoustic transverse Doppler shift?
Hello! I've been looking in modern physics textbooks for a reference to the acoustic transverse Doppler effect. In other words, the Doppler shift that you'd expect to hear if the source was stationary wrt the air, and you were moving past at v m/s, and pointed your rifle mic out at 90 degrees to your direction of motion ... when you hear a quick burst of signal entering your directional mic, what sort of frequency shift should it have? Anyone know of a good reference source that gives the "official" equation for this shift? PS: I know what =I= think it ought to be, but I can't find the damned thing in print. PPS: If modern physics people don't know about the effect, can I lay a claim to it? <grin> =Erk= (Eric Baird) > Hello! > I've been looking in modern physics textbooks for a reference to [quoted text clipped - 9 lines] > equation for this shift? > Acoustic Doppler shifts depend only on the compenent of motion toward or away from the listener, so there is no transverse Doppler shift. > PS: I know what =I= think it ought to be, but I can't find the damned > thing in print. > PPS: If modern physics people don't know about the effect, can I lay a > claim to it? <grin> Since it doesn't exist, you are welcome to it. -E > =Erk= (Eric Baird) >> Hello! >> I've been looking in modern physics textbooks for a reference to [quoted text clipped - 11 lines] > toward or away from the listener, so there is no transverse > Doppler shift. ...unless of course the source were moving fast enough to consider relativistic effects of course, in which case it would be exactly the same as the EM transverse Doppler shift. >> PS: I know what =I= think it ought to be, but I can't find the damned >> thing in print. PPS: If modern physics people don't know about the [quoted text clipped - 6 lines] > >> =Erk= (Eric Baird) > In other words, the Doppler shift that you'd expect to hear if the > source was stationary wrt the air, and you were moving past at v m/s, > and pointed your rifle mic out at 90 degrees to your direction of > motion ... when you hear a quick burst of signal entering your > directional mic, what sort of frequency shift should it have? The rifle mic character implies a very directional microphone, so that hypothetically, source sound is only received when adjacent to the sound source. FYI, the beamwidth of such mics is not so narrow. The sound entering the microphone when adjacent to the source will be the same frequency as emitted since at that position, for an instant, the distance to the source is not changing. However the rate of change of frequency with time will be a maximum, as it is swinging from a higher frequency as you were approaching, to a lower frequency as you soon will be moving further away. > Anyone know of a good reference source that gives the "official" > equation for this shift? See the FAQ file in my web page. This gives accurate values when you are approaching, and when you are receding from, a sound source. For the braodside pass by, the frequency swings from a high frequency to a low frequency. The frequency behavior with time can be calculated according to plane geometry (a simple calculation when your path is a straight line). The velocity used in every case is the rate of change of distance to the source. --------- www.CampanellaAcoustics.com --------- "I have simply studied carefully whatever I've undertaken, and tried to hold a reserve that would carry me through." - Charles A. Lindbergh. "As for background noise level; 35 dBA is a good classroom; 45 dBA is a sound masking system!" - Anthony K. Hoover >Hello! > I've been looking in modern physics textbooks for a reference to [quoted text clipped - 15 lines] > >=Erk= (Eric Baird) Assume a set of axes, the vertical of which is represented by the direction from the source to the microphone and draw on them a vector representing the speed and direction of travel of the source. The length of the Y (cosine) portion of this vector represents the net speed of the source towards (or away from) the microphone at that instant. Add (or subtract when moving away) this to the speed of sound to get the ratio of perceived to actual frequency. Once you have this clear in your head, just derive the actual equation relating angle, velocity and frequency. d _____________________________ http://www.pearce.uk.com >Once you have this clear in your head, just derive the actual equation >relating angle, velocity and frequency. As I said I've already derived it ... I'd just like to be able to find an example of the effect in print in a modern reference book. > Hello! > I've been looking in modern physics textbooks for a reference to [quoted text clipped - 8 lines] > Anyone know of a good reference source that gives the "official" > equation for this shift? You want to be *very* careful about whether this is a relativistic example (light) or a Galilean one (sound). It makes a difference. For velocities at an arbitrary angle theta with ful reativisitic correciton, Jackson gives u_parallel = (u'_parallel + v)/(1+(v dot u')/c^2) u_perp = u'_perp/(gamma_v(1+(v dot u')/c^2)) <http://www.physics.umanitoba.ca/~souther/waves02/feb0402/sld011.htm> "transverse doppler effect" 423 hits "transverse doppler shift" 212 hits  SignatureUncle Al http://www.mazepath.com/uncleal/ (Toxic URL! Unsafe for children and most mammals) "Quis custodiet ipsos custodes?" The Net! A reference to Jackson brings back memories (painful ones) of graduate E&M. Thank for the memory (i think)...RonMan > You want to be *very* careful about whether this is a relativistic > example (light) or a Galilean one (sound). It makes a difference. [quoted text clipped - 10 lines] > "transverse doppler effect" 423 hits > "transverse doppler shift" 212 hits >> Hello! >> I've been looking in modern physics textbooks for a reference to [quoted text clipped - 11 lines] >You want to be *very* careful about whether this is a relativistic >example (light) or a Galilean one (sound). It makes a difference. Indeed. This is for an acoustic calculation, for sound in air, when the transmission medium is stationary wrt the source, but when the detector is moving relative to source and medium at v m/s. As I stated above. >For velocities at an arbitrary angle theta with ful reativisitic >correciton, Jackson gives <SNIP!!!> That's an answer to a different question. I was asking about a simple acoustic effect, sound in air, no use of special relativity involved. >Google >"transverse doppler effect" 423 hits >"transverse doppler shift" 212 hits Yes, but do any of those hits give the ACOUSTIC transverse Doppler prediction? Please read more carefully. =Erk= (Eric Baird) > >> Hello! > >> I've been looking in modern physics textbooks for a reference to [quoted text clipped - 34 lines] > Yes, but do any of those hits give the ACOUSTIC transverse Doppler > prediction? Ditto. There is no acoustic transverse Doppler effect with Galilean transforms. SignatureUncle Al http://www.mazepath.com/uncleal/ (Toxic URL! Unsafe for children and most mammals) "Quis custodiet ipsos custodes?" The Net! <snip> >> Yes, but do any of those hits give the ACOUSTIC transverse Doppler >> prediction? > >Ditto. There is no acoustic transverse Doppler effect with Galilean >transforms. If it makes things any clearer, I've posted an attempt at a trig derivation of the effect in this thread, in a reply to Franz: http://groups.google.com/groups?selm=goks20l20tc7egaiekrf0q7ges8qep4720%404ax.com If we were talking at cross-purposes, that should hopefully clear things up. I /think/ I managed to do it without any dumb mistakes ... but if you do manage to find an accidental sign inversion or something in there, there must be a second mistake further down that cancels it out, because it's the right answer! ;) =Erk= (Eric Baird) > If it makes things any clearer, I've posted an attempt at a trig > derivation of the effect in this thread, in a reply to Franz: [quoted text clipped - 3 lines] > If we were talking at cross-purposes, that should hopefully clear > things up. That's a nice derivation of the collimated detector where rays coming from a certain direction will pass down the collimating tube unimpeded (particle physics). However, if instead a use a line of microphones (to produce the "directional microphone" receiver), along a line parallel to the direction of motion, so that the sound-wave-front is incident on the line of microphones, I think that the only place where such an all-in-phase situation exists is when the array and sound source are both on the line perpendiular to the velocity, V. Angelo Campanella >> If it makes things any clearer, I've posted an attempt at a trig >> derivation of the effect in this thread, in a reply to Franz: [quoted text clipped - 14 lines] >all-in-phase situation exists is when the array and sound source are >both on the line perpendiular to the velocity, V. Hmm. Nice one! Clever! :) But even if you have all these detectors that are /calculated/ to be in phase, you still have to find some way to get all that spatially-distributed information to a particular point, and if we aren't allowed to use electrical wiring (because then we would have an experiment that depends on a hybrid of EM and acoustic signals), we'd need some way to acoustically collect all that information at a single position so that we could verify the phase relationship. That's more difficult. We could try replacing the line with a section of curved reflector that focuses the wavefront on a single microphone (eg one of those parabolic microphones that used to be marketed as kids' toys) ... but again, the focus that we obtain when the reflector and mic are stationary will be messed up when they are moving transversely (presumably, unless you tilt the detector apparatus). ==== I know that some people might argue that the correct way to measure a "transverse" shift is to angle the detector differently depending on speed, but that's not how they actually measure the optical "transverse Doppler effect" in constant-velocity tests. They either aim the detector at 90 degrees in the lab frame and see what the detector reports, or they measure the forward and rearward shifts and derive a sort of "transverse" effect from those two measurements. What they basically do is to say that, if we take the recession shift reported by the experiment and divide out the ratio : f'/f = c/(c+v) , then what remains is interpretable as being a residual "transverse" Doppler shift component. Most direct constant-velocity verifications of the optical transverse effect seem to be done this way. If we apply this same technique to acoustics (and use "s" for the speed of sound in place of "c" for the speed of light), then if the air is stationary wrt the observer, the standard predicted Doppler shift will be: : f'/f = s/(s+v) , and after division, we are left indeed left with a "null" derived transverse effect. But if we carry out the "acoustic" version of the experiment and have the air instead being stationary in the /source/ frame, the standard predicted Doppler shift will instead be: : f'/f = (s-v)/s , and if we divide out the earlier relationship, we are left with a residual frequency-shift effect of: : f'/f = 1 - v^2/s^2 , which is the same "transverse" prediction that we got before for the moving transverse-aimed rifle mic, when the air was stationary wrt the source. So the "acoustic" result does seem to be consistent, using either method. So ... if we follow the constant-velocity methodology used by the "optical" folks to prove an "optical" transverse redshift in light, there's an analogous effect in acoustics, as long as the air is moving wholly or partially with the sound source. The acoustic version of the effect might not be considered to be /theoretically/ interesting, but it does seem to be real. =Erk= (Eric Baird) > Hello! > I've been looking in modern physics textbooks for a reference to > the acoustic transverse Doppler effect. What acoustic transverse effect? The frequency shift depende only on the component of relative velocity along a line between the detector and the source. Franz >> Hello! >> I've been looking in modern physics textbooks for a reference to >> the acoustic transverse Doppler effect. > >What acoustic transverse effect? It's an aberration effect. If a stationary sound source is immersed in still air, and a detector is swept through the region, and the detector is aimed at exactly 90 degrees to its direction of motion, then the portion of the signal that is picked up by that transverse-aimed detector will not be the same portion of signal that was originally projected at 90 degrees to the detector's path by the sound source. So although we can draw a straight line that represents the detector's path, and can argue that the part of the wavefront that hits that path at 90 degrees should be unshifted, the aberration effect means that the /moving/ transverse-aimed detector is actually receiving signals that (according to our stationary reference system) would be intersecting that path at a different angle. >The frequency shift depende only on the component of relative velocity along >a line between the detector and the source. Yep, nicely put. So what we need to do is (a) calculate the aberration angle, (b) calculate the longitudinal component for the angled ray that actually registers on the moving transverse-aimed detector, and then (c) apply the appropriate longitudinal Doppler law to that longitudinal component to get the final freqency shift reported by the equipment. So, in the diagram below, we have a stationary sound source "X" in still air, and a detector "Y" moving from right to left at the bottom of the diagram. The column of "H"'s is a transverse-aimed tube placed over the detector to make sure that sound can only reach it in a particular direction. X / H / <- H / H / H/ Y <- <----v---- If the signal from X enters the tip of the tube, then by the time it reaches the detector at the far end, the tube will have moved further to the left, so the signal that successfully passes through the tube to the detector without touching the tube sides is actually moving along the line marked out by the diagonal "/" marks. So, if we say that the speed of sound is "s" m/s, and that the sound happens to take one second to reach the detector then we have a right-angled triangle with baseline v metres and hypoteneuse c metres, and the ray that will be intercepted and detected will be one that is offset from 90 degrees by an aberration angle "A", where : SIN(A) = v/s Now, when we stand at X and look along this diagonal line towards the microphone at Y, the mic is partly moving across our field of view and partly receding, and the velocity's recession component "w" would then seem to be : : w = v SIN(A) , \ w / \ <----v----|A , and since we've just said that SIN(A) = v/s, our recession velocity component is: : w = v * v/s : w = v^2/s Finally, since the Doppler formula for a "stationary" source and a "moving" observer receding at v is : : freq'/freq = 1 - v/s , we can say that our recession component w should be responsible for a shift showing up on our transverse-aimed moving microphone of : freq'/freq = 1 - w/s : freq'/freq = 1 - v^2/s^2 :==SUMMARY== So ... if the above calculations aren't screwed up, they seem to say that if we fix together an array of four microphones each pointing outwards at 90 degrees to its neighbours and forming the shape of a cross, and move that mic assembly through the air along a straight-line path aligned with two of those mics, and our sound sources are stationary wrt the air, the "forward" and "rearward" mics should show shifts of : freq'/freq = 1 +/- v/s , and the two side mics should show a frequency reduction of : freq'/freq = 1 - v^2/s^2 , and that's your acoustic transverse Doppler effect. =Erk= (Eric Baird) > >> Hello! > >> I've been looking in modern physics textbooks for a reference to [quoted text clipped - 10 lines] > same portion of signal that was originally projected at 90 degrees to > the detector's path by the sound source. That is not a transverse Doppler shift. The TDS is a purely relativistic effect which occurs with light propagation only. Aberration and Doppler shifts are entirely separate phenomena > So although we can draw a straight line that represents the detector's > path, and can argue that the part of the wavefront that hits that path [quoted text clipped - 7 lines] > > Yep, nicely put. In other words, you agree that there is no transverse Doppler effect in the case of sound. In the case of light, there actually *is* a Doppler shift which occurs when the source is moving *at right angles* to the line of sight. It is a purely relativistic effect. [snip] The stuff I snipped has nothing to do with the transverse Doppler shift. Franz >> >> Hello! >> >> I've been looking in modern physics textbooks for a reference to [quoted text clipped - 12 lines] > >That is not a transverse Doppler shift. It is a Doppler shift that is present in a signal from a detector that is aimed at 90 degrees to the direction of motion wrt a source. It may not be the /same/ transverse Doppler shift that you are familiar with from textbooks, but that's not the same as saying that the effect does not exist. >The TDS is a purely relativistic effect which occurs with light propagation >only. Those supplied calculations say otherwise. >Aberration and Doppler shifts are entirely separate phenomena They are quite intimately related, actually >> So although we can draw a straight line that represents the detector's >> path, and can argue that the part of the wavefront that hits that path [quoted text clipped - 11 lines] >In other words, you agree that there is no transverse Doppler effect in the >case of sound. No. I would agree that the simple calculation for Doppler effects on a detector moving past a source (with the detector pointing at 90 degrees to the direction of motion), should give us a "no shift" prediction when the sound-carrying medium has no motion wrt our detector (the "moving source" or "stationary detector" case). But if the sound-carrying medium is instead stationary wrt the sound /source/, (i.e. the "moving detector", or "stationary source" case), then I calculate that the same detector should pick up a signal whose frequency is reduced by the factor : freq'/freq = 1 - vv/ss So, in the case of sound, in some situations there is no predicted Doppler effect on the transverse-aimed detector, and in other cases there is a predicted frequency-reduction, depending on how the air is moving wrt the source and detector. If the air moving in the direction of the detector path, but at an intermediate velocity, then we should get an similarly-intermediate frequency drop in the audio signal received. >In the case of light, there actually *is* a Doppler shift which occurs when >the source is moving *at right angles* to the line of sight. It is a purely >relativistic effect. and yet ... if you actually do the audio calculations for a "stationary" source and a "moving" sensor, you will find an analogous effect for audio, when the sensor is set up to point at right angles to its direction of motion. That's the calculation that I provided you with. If you choose not to look at it, that is entirely up to you. >[snip] > >The stuff I snipped has nothing to do with the transverse Doppler shift. Ah. the words "_THE_ transverse Doppler shift" (emphasis added), rather presuppose that there can only be /one/ transverse Doppler effect, don't they? But how do you know there /is/ only one, until you've done the calculation? I would suggest that if you are at all interested in the subject of Doppler effects, you may like to forget official "syllabus physics" for a few minutes, and try the actual math. You may find it a liberating experience. Physics is not like "bible studies", the reference works are occasionally allowed to be misleading (or even wrong sometimes). Hopefully it doesn't happen very often, but it does happen. =Erk= (Eric Baird) > >> >> Hello! > >> >> I've been looking in modern physics textbooks for a reference to [quoted text clipped - 27 lines] > > They are quite intimately related, actually Aberration is an effective shift in source direction Doppler effect is a change in frequency of a moving source. They are related only insofar as both are phenomena associated with moving sources. There is no transverse Doppler shift. The frequency shift is a function purely of the source frequency measured in coordinates moving with the source, and the line-of-sight componenet of the relative velocity between the source and the observer. > >> So although we can draw a straight line that represents the detector's > >> path, and can argue that the part of the wavefront that hits that path [quoted text clipped - 13 lines] > > No. Sorry, but then you are out on a limb, and I cannot help you any more. Goodbye [snip] Franz |
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