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Question

An air column in a tube 32 cm long, closed at one end, is in resonance with a tuning fork. The air column in another tube, open at both ends, of length 66 cm is in resonance with another tuning fork. When these two tuning forks are sounded together, they produce 8 beats per second. Then the frequencies of the two tuning forks are:
(Consider fundamental frequencies only)

A
250 Hz,258 Hz
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B
240 Hz,248 Hz
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C
264 Hz,256 Hz
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D
280 Hz,272 Hz
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Solution

The correct option is C 264 Hz,256 Hz
Since v=nλ and velocity in two cases must be same as the medium is same. λ1=4(32) cm=128 cm and λ2=2(66) cm=132 cm.

Hence, n1n2=λ2λ1=132128=3332.

Also, n1n2=8,

Solving these gives n1=264Hz and n1=256Hz.

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