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Question

Two organ pipes sounded together to give 5 beats per second. If their length is in the ratio of 50:51, then the frequency of shorter and longer pipes are respectively

A
250,245
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B
245,250
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C
250,255
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D
255,250
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Solution

The correct option is D 255,250
Let nA and nB be the frequency of the organ pipes A and B respectively.
We have nA=VAlA and nB=VAlB
V= Velocity of sound in air
lA= Length of the air column resonating with pipe A
lB= Length of the air column resonating with pipe B
nAnB=lAlB=5150 (given) (equation 1)
Since both pipes together produce 5 beats per second,
nAnB=5 (equation 2)
By solving equation 1 and 2 we get
nA=255Hz and nB=250Hz

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