A tuning fork of frequency 512 hZ makes 4 beats per second with the vibrating string per sec when th

Question

A tuning fork of frequency 512 hZ makes 4 beats per second with the vibrating string per sec when the tension in the piano string is slightly increased. The frequency of the piano string before increasing tension was

Accepted Answer

Let the frequency of tuning fork and piano string be

respectively
∴

= 516 Hz or 508 Hz
Increase in the tension of a piano string increases its frequency.
If

= 516 Hz, further increase in

, resulted in decrease in the beat frequency. But thisis not given in the question.
If

= 508 Hz, further increase in

resulted in decrease in the beat frequency. This is given in the question. When beat frequncy decreases to 2 beats per second.
Therefore, the frequency of the piano strings before increasing the tension was 508 Hz.

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