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B Sound waves and speed of it in different reference frames

  1. Jul 1, 2016 #1
    Think at a cop car with a siren that moves with a velocity Vc, it emits a sound with a velocity C

    Now think about a person that doesn't move, in front of the cop car, shouldn't he register that the speed of the sound emited is Vs= Vc+ C?

    According to the galileian equations (true for v <<c light)

    x= x' + Vc t (distance done by the sound wave according to the guy in front of the cop car)
    x'= Ct (distance done by the sound wave according to the cop car frame of reference)

    x= (C+ Vc) t

    d/dt x = d/dt [ (C+Vc) t]

    Vs= C + Vc

    Is that correct? Does the speed of the wave change with the frame of reference?

    Is because of that that the frequency changes? (Doppler effect)
  2. jcsd
  3. Jul 1, 2016 #2

    Doc Al

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    Staff: Mentor


    Realize that the speed of sound is C with respect to its medium, the air. So a person at rest with respect to the air will measure the speed of the sound as C.
  4. Jul 1, 2016 #3
    and... the cop? Why is he registering the same speed?

    Ain't the cop and the person in relative motion?
  5. Jul 1, 2016 #4

    Doc Al

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    Staff: Mentor

    He's not. Here's the basic formula:
    Speed of sound with respect to cop = Speed of sound w.r.t. air + speed of air w.r.t cop = C - Vc.

  6. Jul 4, 2016 #5
    Basically, it will travel slower relative to the car and the speed of sound relative to the ground
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