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

Answer

C

Explanation

`f_(1) = 256 Hz`
For tuning fork, where `f_(2)- f_(1) = pm 5`
`f_(2) =` frequency of piano
`f_(2) = (256 + 5)Hz or (256 - 5)Hz`When tension is increased, the beat frequency decreases to 2 beats per second.
If we assume that the frequency of piano string is 261 Hz, then on increasing tension, frequency, more than 261 Hz. But it is given that beat frequency decreases to 2, therefore 261 Hz is not possible,
Hence, 251 Hz i.e., (256 – 5) was the frequency of piano string before increasing tension.