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Question

An air column at temperature of 51C produces 4 beats in one second with a tuning fork.
When the temperature of the air column decreases to 16C then one beat per second is produced with same tuning fork. The frequency of the tuning fork is

A
80 Hz
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B
70 Hz
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C
60 Hz
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D
50 Hz
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Solution

The correct option is D 50 Hz
Let us suppose, the frequency of the tuning fork is fo and the frequency of the sound source in the air column is f.
So, beat frequency,
fb=|fof|
At 51 C, fb=4 Hz
At 16 C, fb=1 Hz
As temperature reduces, beat frequency reduces, hence
we can write fb=ffo
Let f1 be frequency at 51 C, f2 be frequency at 16 C,
f1=4+fo and
f2=1+fo
We know that fT
f1f2=T1T2=324289=1817=4+fo1+fo
18+18fo=68+17fo
fo=50 Hz

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