A metal wire of diameter 1mm is held on two knife edges separated by a distance of 50cm . The tension in the wire is 100 N. the wire vibrates with its fundamental frequency and a vibrating tuning fork together produce 5 beat/s. The tension in the wire is the reduced to 81N. When the two are excited , beat are heard at the same rate, then the frequency of the fork will be ,

Options

A. 45 Hz
B. 95 Hz
C. 100 Hz
D. 50 Hz

Answer

B

Explanation

`n_1 gt N gt n_2`
`therefore n_1 - N " and " N-n_2 = 5`
`n_1 - n_2 =10 " "….(i)`
`n_1 prop sqrt(T_1) " and " n_2 prop sqrt(T_2)`
`therefore n_1/n_2 = sqrt(T_1/T_2) therefore n_1/n_2 = 10/9`
`n_1 = 10/9 n_2`
Substitute `n_1` is equation (i), we have
`10/9 n_2-n_2 = 10 therefore n_2=90`
`N=n_2+5 = 90+5 = 95Hz`