A sonometer wire of length 65cm is in resonance with a tuning fork of frequency N. If the length of the wire is decreased by 1cm and it is vibrated with the same tuning fork, 8 beats/s are heard, then the frequency of the tuning fork will be

Options

A. 256Hz
B. 384Hz
C. 480Hz
D. 512Hz

Answer

D

Explanation

`n_2-n_1 = 8 " " ….(i) " " n_1l_1=n_2l_2`
`n_1/n_2 = l_2/l_1 = 64/65 therefore n_1 =64/65 n_2`
Substitute `n_1` is eqn(i), we have ,
`n_2-64/65n_2 = 8 therfore 65n_2-64n_2 = 8xx65`
`therefore n_2=520`
`therefore n_1 = n_2-8 = 520 -8 = 512 Hz`