Question

A tuning fork of frequency 512 Hz makes 4 beats//s with the vibrating string of a piano. The beat frequency decreases to 2 beats//s when the tension in the piano string is slightly increased.The frequency of the piano string before increasing the tension was
A. `510 Hz`
B. `514//Hz`
C. `516 Hz`
D. `508 Hz`

Answer 1

Correct Answer - D
Suppose `n_p=` frequency of piano`=?`
`(n_(p)sqrtT)`
`n_f=` frequency of tuning fork `=512Hz`
`x=`beat frequency `=4beats//s`, which is decreasing `(4rarr2)` after changing the tension of piano wire. Also, tension of piano wire is increasing so `n_(p)uarr`
Hence, `n_(p)uarr-n_f=xdarrrarr`wrong
`n_f--n_(p)uarr=xdarrrarr` correct
`impliesn_p=n_f-x=512-4=508Hz`