Question

A bat flies toward a wall, emitting a steady sound of frequency 2030 Hz . The bat hears its own sound, plus the sound reflected by the wall.

Part A

How fast should the bat fly in order to hear a beat frequency of 20.0 Hz ?

Answer 1

The apparent frequency at the wall is given by

f = [(c + vr)/(c + vs)]*f0

here c=speed of sound, vs is the speed of source(positive if source moves away from observer). vr is the velocity of reciever=0 in this case.

f= 344*2030/(344-vs)

now the wall emits sound with this frequency and bat is the reciever and is moving with vr= vs

f=344*2030/(344-vs) *(344+vs)/344=2030*(344+vs)/(344-vs)

For beat frequency of 20,

f-f0=20

2030*(344+vs)/(344-vs) - 2030 = 20

vs =1.68 m/s