Question

A woman holds a tuning fork that vibrates at frequency 0 f while she runs horizontally toward a vertical wall at speed w v . The speed of sound is v. She holds the tuning fork in such a way that the smooth wall reflects the sound perfectly. This reflection produces a Doppler shift in frequency, equivalent to what would happen if there were a second woman on the other side of the wall running toward the original woman.

What beat frequency does the woman detect (in terms of the given quantities)?

Answer 1

Answer: The beat frequency detect by the woman is f0 [ 2v / ( v - vW) ]

Step-by-step explanation:

given a Doppler effect,

the frequency heard by the listener in terms of frequency of source is expressed as;

fL = [ (v + vL) / (v + vS) ] fS

vL is the velocity of the listener, vS is the velocity of the source and V is the velocity of sound.

Now What beat frequency does the woman detect (in terms of the given quantities)?

The wall will receive and reflect pulses at a frequency of;

fWALL =( v / (v - v0)) f0

so the woman will hear this wave;

fWOMAN = ((v + vW) / v) ( v / (v - vW)) f0

fWOMAN = (( v + vW) / ( v - vW)) f0

Now the beat frequency will be;

fBEAT = ((v + vW) / (v - vW)) f0 - f0

fBEAT= f0 [ ((v + vW) / (v - vW)) - 1 ]

fBEAT= f0 [ 2v / ( v - vW) ]

The beat frequency detect by the woman is f0 [ 2v / ( v - vW) ]