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Doppler effect and amplitude

  1. Jun 23, 2011 #1
    Does the amplitude of a wave changes when the source is moving? I am mainly interested in waves in a medium (e.g. sound, water...)

    No text about Doppler effect I have found mentions anything about the amplitude so I guess it does not change.

    However in the case if the speed of the source is equal to the wave, I think, if there where N wavefronts emitted the amplitude should be N-times larger than that of one amplitude (see http://upload.wikimedia.org/wikipedia/commons/2/25/Mach_cone.svg" [Broken] (the case Ma=1)).

    If the speed of the source is slightly below the wave speed, the amplitude should be slightly lower than N-times and so on...

    So I get the feeling that the amplitude does indeed change.

    What's correct, what's wrong? Why? It would be great if someone has a detailed explanation!
     
    Last edited by a moderator: May 5, 2017
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  3. Jun 23, 2011 #2

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  4. Jun 23, 2011 #3
    Thanks for the answer. However I don't see why the amplitude is not affected in the case when the source moves slower than sound speed?
     
  5. Jun 23, 2011 #4

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    Well, I may not have a foolproof explanation, but here is what I can offer.

    Sound is a harmonic wave, just like a mass on a spring that oscillates, or a pendulum.
    It has a certain energy that does not change when it is in motion.

    A sound wave has a certain energy that dissipates as a sphere (in air) with the square of the distance.
    The energy is independent of the frequency, but is linearly related to the square of the amplitude.
    In particular this means that the amplitude decreases with the square of the distance travelled (in air).

    This does mean of course that the amplitudes will be higher in the direction in which the sound source travels, but only as related to the distance the sound has travelled from its origin.
     
  6. Apr 6, 2012 #5
    great question!
    i have been doing thought experiments on this for years, and i find every few months i decide the opposite way. It seems intuition alone wont solve this, and i have been pondering about many experiments to setup to find out one way or another but i have not done it.

    i have always thought that amplitude must be effected by dopler, exactly as you describe it, if you match the speed of transmission then you must be continually dumping more energy into that point in space-time (although moving, following the energy), to dump more in, and so on.

    which leads me to also ponder what is the maximum energy you could pump into a particular moving pocket of energy in a transmission.

    which makes me think this is something of a way of thinking which makes it obvious that a sonic boom would occur when exceeding the speed of sound, and so what is an electromagnetic boom ?

    fascinating question, if you ever do/did find an answer id love to know!

    i search 'dopler amplitude' and related terms often, and never find anything close to an answer, but finally at least i found your question which has been the most on-topic i have ever found on this subject!

    so without anwering you, i registered just to say that, thanks! :)
     
  7. Apr 6, 2012 #6

    haruspex

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    If you take a snapshot of the waveform in the case where the speed is a bit below the speed of sound you'll see the N waves close together but each with its initial amplitude. You seem to feel that since each peak has 'caught up' the preceding one a bit it somehow makes it grow, but you're overlooking that the intervening trough has caught it up just as much, proportionally.
    At the speed of sound, the snapshot does not show one wave with N times the magnitude. It shows no bow wave at all! It now only exists as a variation in pressure over time right at the source. So in your gut feel view you're not comparing waves that exist in the same sense.
     
  8. Apr 6, 2012 #7

    sk9

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    well considering that we cant reach speed of EM waves it is safe to say that there are no chance of EM boom but what i think is what happens in case of transverse wave when its source moves faster than the speed of wave? .eg in case of wave on a string (i cant even imagine)

    As far as the sources velocity is less than that of sound i see no reason that its amplitude should not change in the same way if it was stationary.
     
  9. Apr 7, 2012 #8
    This is a good question, I think you are in general almost right. Remember that for an EM wave the frequency increases, an increase in frequency will result in an increase in energy. So although the amplitude does not increase the rate of energy deposition will.

    I don't know about sound waves - I don't know how change in frequency affects wave energy. The physics of sound waves approaching the speed of sound is called 'weak shocks' if anyone want to read more.

    Finally, sk9, there is such thing as an 'EM sonic boom', things can travel faster that light in a medium- look up Cherenkov Radiation.
     
  10. Apr 7, 2012 #9

    sk9

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    i am sorry for my ignorance. i actually once wondered about speed of light in high refractive index but had never related it to Cherenkov Radiation. so thanks.
     
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