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.

Solve including equations used and the work from one step to the next please and thank you

Explanation / Answer

a) let my velocity be v.

By Doppler effect, I must hear one frequency go up and the other come down.

the higher frequncy heard = (1+v/343)*229 Hz the lower frequency = (1-v/343)*229 Hz

So by problem 2v/343*229 = 2.5, hence v= 3.745 m/s

b) the new beat frequency will be (2*3.745)/343*229 = 5Hz

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