A tuning fork of known frequency `256 Hz` makes `5` beats per second with the vibrating string of a piano. The beat frequency decreases to `2` beats per second when the tension in the piano string is slightly increased. The frequency of the piano string before increasing the tension was

Options

A. `(256 + 5) ` Hz
B. `(256 - 5)` Hz
C. `(256 - 2)` Hz
D. `(256 + 2)` Hz

Answer

B

Explanation

Since there are 5 beats / sec , the initial frequency of the piano string is either
` (256 + 5 ) Hz = 261 Hz " or " (256 - 5) Hz = 251 ` Hz
For a piano string , ` n = 1/(2 l) sqrt(T/m) " i.e. : n propto sqrtT`
Thus when T is increased , n will increase.
Hence if ` n = 261 ` Hz, the frequency will increase and the number of beats /sec will increase. Hence it cannot be 261 Hz. But if it is 251 Hz, and becomes 254 after increase, we will get 2 beats / sec.
` :. ` The correct frequency is ` (256 - 5)` hz.