Two speakers, 15 m apart, are facing each other producing identical 229 Hz sound

Question

Two speakers, 15 m apart, are facing each other producing identical 229 Hz sounds. You walk away from one speaker, towards the other, and you hear what sounds like beats at a frequency of 2.5 Hz. (a) How fast are you walking? (b) If the frequency of the sound emitted is increases to 573 Hz and you continue to walk at the same speed, what frequency of beats will you hear? (Hint: You can model this situation as a tube open at both ends; alternatively, you can treat it as a Doppler effect problem.)

Explanation / Answer

F'= ((V+Vr)/(V+Vs))f

V= velocity of sound in air

Vr= Velocity of receiver

Vs= velocity of source

now for beat frequency

f'= ((V+Vr)/V-(V-Vr)/V)*f

2.5= 2Vr/V*229

Vr= 1.88m/sec

b.) f'= (2*1.88/345)*573

= 6.245 Hz

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