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Doppler effect, sound source and reflecting surface moving towards eachother

  1. Nov 8, 2011 #1
    1. The problem statement, all variables and given/known data

    A sound source A and reflecting surface B move directly towards each other. Relative to the air the speed of source A is 29.9 m/s, the speed of the surface B is 65.8 m/s and the speed of sound is 329m/s. The source emits waves at frequency 1200 Hz as measured in the source frame. In the reflector frame, what are the (a) frequency and (b) wavelength of the arriving sound waves? In the source frame, what are the (c)frequency and (d) wavelength of the sound waves reflected back to the source?

    va=29.9 m/s
    vb=65.8 m/s
    v=329 m/s
    f=1200Hz

    2. Relevant equations
    f'=f(v+vd)/(v-vs) since they are moving towards each other
    wavelength λ=v/f

    3. The attempt at a solution
    (a) did relative speeds since the want the relative to different frames
    source B is detector

    source A relative to B: v = 29.9- (-65.8) = 95.7 m/s
    source B relative to B: v = -65.8 - (-65.8)= 0 m/s (which makes since relative to itself of course it wouldn't be moving)

    f'=(329 + 95.7)/(329-0) *(1200Hz) = 1549 Hz

    (b) λ =v/f = 329/ 1549

    (c)source a as detector
    source b relative to a: v= 95.7 m/s
    source b relative to b: v=0m/s
    f'=(329 + 95.7)/(329-0) *(1200Hz) = 1549 Hz

    is this right? and then the wavelength will be the same? the reflected waves move at a constant speed right, so the speed of the reflected wave relative to air should be the same, right? or do i use 1549Hz as frequency in part c?

    Thank you for your help.
     
  2. jcsd
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