Posted by Elisa on Wednesday, August 6, 2008 at 12:09am.
Yes, you have to use Doppler shift equations twice; first to get the frequency received and reflected by the insect in its own frame of reference,l then to consider the insect a moving source of that frequency, and calculate the still higher frequency received by the bat.
Since the speeds are small compared to the speed of sound, you can get an accurate approximation by assuming the insect is still and the bat moves toward it at 4 m/s, resulting in an upwards Doppler shift of
delta f = fo * 2 * (4/340)
4/340 is the relative Doppler shift, fo the emitted frequency, and the factor of two accounts for the two Doppler shifts, sending and receiving.
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