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Question

Two tuning forks A and B are sounded together and 7 beats/s are heard. A is in resonance with a 32 cm air column closed at one end and B is in resonance when length of air column is increased by 1 cm. The frequencies of forks A and B are

A
264 Hz, 256 Hz
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B
272 Hz, 264 Hz
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C
231 Hz, 224 Hz
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D
220 Hz, 512 Hz
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Solution

The correct option is A 231 Hz, 224 Hz
Tuning fork A :
Length of closed air column LA=32 cm=0.32 m
Frequency of tuning fork A νA=v4LA=v4(0.32)
Tuning fork B :
Length of closed air column LB=33 cm=0.33 m
Frequency of tuning fork B νB=v4LB=v4(0.33)
Beat frequency b=νAνB
7=v4(0.32)v4(0.33)
v=295.7 m/s
Frequency of tuning fork A νA=295.74(0.32)=231 Hz
Frequency of tuning fork B νB=295.74(0.33)=224 Hz

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