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

To frequency of the vibrating string with respect to tuning fork is either `(256+5)Hz or (256-5)Hz`
`(256+5)Hz and (256-5)Hz`
`f_("wire")=(1)/(2l)sqrt((T)/(mu))`
On increasing tension , the beat frequency decreases to 2 Hz, so probable frequency of the wire with respect to fork none is
But on increasing the tension of wire, the frequency of the wire must have to increase. So, if the original frequency of the wire is assumed to be 261 then it readuces to 258 whereas if it is assumed to be 251 it has increased to 254. As we were expecting increase, so the correct frequency of the piano wire is (256 -5)Hz.