A speaker fixed to a moving platform moves toward a wall, emitting a steady sound with a frequency of 235 Hz . A person on the platform right next to the speaker detects the sound waves reflected off the wall and those emitted by the speaker. How fast should the platform move for the person to detect a beat frequency of 6.00 Hz ?
Take the speed of sound to be 344 m/s .

vr = 4.336 m/s

Explanation:

We are given that;

Beat frequency is 6Hz

Speed of sound = 344 m/s

Now,

Reflective Doppler frequency; f = 235 + 6 = 241 Hz

We can calculate the observed frequency if both the source sound and the observer are moving towards each other. In this case, the formula is:

f = fo[(c + vr)/(c + vs)]

Where;

ƒ = observed frequency

c = speed of sound

vs = velocity of source (negative if it’s moving toward the observer)

ƒ0 = emitted frequency of source

Since it’s moving toward the observer, thus we can rewrite equation as;

f = fo[(c + vr)/(c - vs)]

We have that;

fo = 235 , f = 241 , c = 344 , vr=vs

Thus,

241 = 235[(344+vr)/(344-vr)]

241(344 - vr)= 235(344 + vr)

82904 - 241vr = 80840 + 235vr

82904 - 80840 = 241vr + 235vr

2064 = 476 vr

vr = 2064/476

vr = 4.336 m/s

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