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Question

Given figure shows a sound filter in which sound is passing through a bifurcated pipe. Speed of sound in air is 300 m/sec. A sound consists of four frequencies 300 Hz,600 Hz,900 Hz,1500 Hz.
Then which of the following frequency will pass through outles


A
300 Hz
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B
600 Hz
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C
900 Hz
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D
1500 Hz
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Solution

The correct option is B 600 Hz
The frequency of sound waves, for which destructive interference occurs will result into a net zero intensity of resultant sound. Hence these waves will not pass through filter.
Condition for destructive interference (Minimum Intensity),
Δ x=(2n+1)λ2...(i)
The path difference between waves arriving through two routes of the bifurcated pipe is,
Δ x=x2x1
Δ x=(25+25+25) cm25 cm
Δ x=50 cm=0.5 m
From Eq. (i),
(0.5×2)=(2n+1)λ
1=(2n+1)Vf
f=(2n+1)V=(2n+1)300
For (n=0, 1, 2, ... etc) we get:
f=300 Hz, 900 Hz, 1500 Hz,...etc
Hence odd multiples of 300 Hz will not pass through filter.

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