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? You can answer part (a) with either a standing wave model or as Doppler shift effect. (c) Answer part (a) using the method you did not use.

Explanation / Answer

(a)

fbeat = f(v+vr)/v - f(v-vr)/v , (As v = 340 m/s)

2.5 = 229(340 + vr) / 340 - 229(340 - vr) / 340

850 = 229vr + 229vr

458vr = 850

vr = 1.856 m/s

(b)

fb = 573(340 + 1.856) / 340 - 573(340 - 1.856) / 340

340fb = 573*1.856*2 = 2126.976

fb = 6.26Hz

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