In a sonometer experiment the bridges are separted by a fixed distance the wire which is slightly elastic emits a tone of frequency n when held by tension T If the tension is increased to 4T the tone emitted by the wire will be of frequency

Options

A. n
B. 2n
C. slightly greater than 2n
D. slightly less than 2n

Answer

D

Explanation

For a sonometer wire ,
`n = 1/(2L) sqrt(T/m) = 1/(2L) sqrt(T/(pir^(2) rho)) = 1/(2Lr) sqrt(T/(pirho)) `
i.e. `n propto sqrtT` , when T is increased to 4 times, n should be doubled i.e. n' = 2n.
But because the wire is elastic, increase in tension, increases the length and ` :' propto 1/L `, there is a slight decrease in frequency. Hence the note emitted by the wire will be frequency slightly less than 2n.
There is a small decrase in radius, which will increase the frequency (n). But this effect is negligible as compared to the effect of length.