Question

# A closed organ pipe and an open organ pipe of same length produce 2 beats/second when they are set into vibrations together in fundamental mode. The length of open pipe is now halved and that of closed pipe is doubled. The number of beats produced will be

A
7
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B
4
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C
8
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D
2
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Solution

## The correct option is A 7For a closed organ pipe, the frequency of fundamental mode isνc=v4Lcwhere v is the velocity of sound in air and Lc is the length of the close pipe.For an open organ pipe, the frequency of fundamental mode isνo=v2Lowhere Lo is the length of the open pipe.Given, Lc=Lo∴νo=2νcand νo−νc=2 Solving the above equations we get:-νo=4 Hzνc=2 HzWhen the length of the open pipe is halved, its frequency of fundamental mode isν′o=v2(Lo2)=2νo=2×4 Hz=8 HzWhen the length of the closed pipe is doubled, its frequency of fundamental mode isν′c=v4(2Lc)=12vc=12×2 Hz=1 HzHence, Number of beats produced per second =ν′o−ν′c=8−1=7

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