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Bat echolocation - doppler effect

  1. Sep 11, 2006 #1
    Hi, this is the question:
    A bat flies toward a wall, emitting a steady sound with a frequency of 22.5 kHz. This bat hears its own sound plus the sound reflected by the wall.

    How fast should the bat fly, v_b, to hear a beat frequency of 225 Hz?

    Take the speed of sound to be 344m/s.

    This is what I've done so far:

    I've found the frequency that the bat hear when it echoes off the wall. I
    got the equation... Fbat = Fo ((v_w + v_b) / (v_w - v_b)) where Fbat is
    the frequency that the bat will here off of the wall, Fo is the original
    emittance frequency from the beginning, and v_b is the velocity the bat
    should be traveling in.

    I've then solved for v_b... rearranging the formula. But from there, I'm not too sure how to incorporate the "beats" idea.

    I also believe the beat frequency formula is f_beat = f_1 - f_2 = 225 Hz.

    As far as this problem goes, that's all I know how to do - I'm stuck at
    this point. Could you help me out?
  2. jcsd
  3. Sep 12, 2006 #2
    You are given that f_beat=225Hz, f_1=22500Hz

    f_2 is your Fbat so that means f_2=Fo ((v_w + v_b) / (v_w - v_b))

    Plug all of this into the equation f_beat=f_1-f_2:
    225Hz=22500Hz-Fo ((v_w + v_b) / (v_w - v_b))
    Fo and v_w are known so you can just solve for v_b
  4. Nov 11, 2007 #3
    i tired.. but i cant get the right answer
  5. Nov 11, 2007 #4
    You have to use the Doppler equation twice for this problem; once for the sound emitted by the bat to the wall, and a second time for the sound reflected from the wall to the bat.
  6. Nov 11, 2007 #5
    what do you mean by that?
  7. Nov 11, 2007 #6
    The sound heard by the bat is not just the sound "heard" by the wall. He will need to do two equations, one where the source is the bat and the listener is the wall, and one where the source is the wall, and the listener is the bat.
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