The string of length L is stretched by x when the speed of transverse wave along it is `v_1`. The string is further stretched by `Delta x` when the speed of transverse wave along it is `v_1sqrt(2)`. Find `Delta x`:

Options

A. `(sqrt(2)-1)x`
B. `xsqrt2`
C. `x`
D. `(sqrt2+1)x`

Answer

C

Explanation

`v=sqrt(T)/(mu) rArr v prop sqrtT`
and stress `prop Delta l`
Hence `(T_(1))/(T_(2)) =(x)/(x+Deltax) =[(V_(1))/(V_(2))]^(2)`
`(x)/(x+Deltax) = [sqrt2]^(2) rArr x = 2 (x + Delta x)`
`rArr x= Delta x`.