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)

Answer 1

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 ,

$n\pm 256=4$ ,

or $n=256\pm 4=252$ 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 .