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Question

A tuning fork produces 4 beats per second with another tuning fork of frequency 256 Hz. The first one is now loaded with a little wax and the beat frequency is found to increase to 6 per second. What was the original frequency of the first tuning fork. (in Hz)

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Solution

Let the original frequency of first tuning fork is n , frequency of other fork is 256Hz ,
given that the , beat frequency is 4/s ,
therefore ,
n±256=4 ,
or n=256±4=252 or 262Hz ,
if the frequency of first fork is 260Hz , on loading with wax , its frequency decreases and difference in frequency (beat frequency) should decrease , but it is not happening , so 260Hz is not the frequency of first fork .
if the frequency of first fork is 252Hz , on loading with wax , its frequency decreases and difference in frequency (beat frequency) should increase , but it is now happening as the beat frequency is now 6/s , so 252Hz is the original frequency of first fork .

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