Turning fork A of frequency 305 Hz produces 5 beats `s^(-1)` with another turing fork B. After filling tuning fork B, it produces 3 beats `s^(-1)` with A. The frequency of B before filling was

Options

A. 300 Hz
B. 313 Hz
C. 310 Hz
D. 308 Hz

Answer

A

Explanation

The phenomenon of beats is used in the determination of unknown frequencies.
Suppose `v_(2)` is the unknown frequency of a tuning fork B. Let this fork B produce m beats per second with another tuning fork A of known frequency `v_(1)`, As number of beats/s is equal to difference in frequency of two sources.
Therefore, `v_(2) = v_(1) +- m`
When the prong of fork B is filed a little, it becomes lighter and its frequency of vibration increases on sounding the filed fork B with fork A, we count the number of beats `s^(-1)`. Proceeding as, we conclude that, if number of beats `s^(-1)` on filing fork B of unknown frequency increases, m would So, frequency of tuning fork B
`= 305 +- 5 = 310 Hz, 300Hz`
Since, on filing tuning fork B, number of beats decreases. This means that frequency of B should be less ie, 300 Hz