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Question

A closed pipe and an open pipe of same length produce 2 beats, when they are set into vibration simultaneously in their fundamental mode. If the length of the open pipe is halved and that of closed pipe is doubled, and if they are vibrating in the fundamental mode, then the number of beats produced is:

A
4
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B
7
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C
2
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D
8
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Solution

The correct option is B 7
For closed pipe
fc=v41o fundamental frequency fc
For open pipe
fo=v21o fundamental frequency
fofc=2v21ov41o=2v410=2.....(i)
Case -II
lc=2lc while lopen=lo2
fc=v4×2lo=v8lofo=v2×lo2=vlofofc=xvlov8lo=x7v8lo=x......(ii)
x=7 by (i)and (ii)

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