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Question

Two tuning forks P and Q sounded together and 6 beats per second are heard. P is in unison with a 30 cm air column open at both ends and Q is in resonance when length of air column is increased by 2 cm. The frequencies of forks P and Q are

A
90 Hz and 84 Hz
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B
100 Hz and 106 Hz
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C
96 Hz and 90 Hz
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D
206 Hz and 200 Hz
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Solution

The correct option is C 96 Hz and 90 Hz
We know that f=v2I
(Fundamental frequency of an open organ pipe).
Number of beats heard =6
fPfQ=6
or v2(0.3)v2(0.32)=6
or v=2×0.3×0.32×60.320.3
Now, fP=v2(0.3)=0.32×60.02=96 Hz
and fQ=v2(0.32)=0.3×60.02=90 Hz.

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