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Question

Two sound sources S1 and S2 emit pure sinusoidal waves in phase. If the speed of sound is 330 m/s, then for what frequencies does constructive interference occur at P?


A
500 Hz
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B
1000 Hz
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C
1200 Hz
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D
1500 Hz
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Solution

The correct option is D 1500 Hz
Let O be the midpoint between S1 and S2.
Seperation between two sound sources S1S2=4.68 m
Path difference, Δx=|S1PS2P|
From the data given in the question,

Δx=(32+4242+1.682)=54.3380.66 m
Condition for constructive interference to occur,
Δx=nλ=n(vf) [where n=1,2,3,....]

f=nvΔx=n×3300.66f=500n Hz

For n=1 , f=500 Hz
For n=2 , f=1000 Hz
For n=3 , f=1500 Hz
and so on.
Thus, options (a), (b) and (d) are correct answers.

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