If the tension in a stretched string fixed at both ends is changed by `21%` , the fundamental frequency is found to increase by `15 Hz`, then the

Options

A. original frequency is `150 Hz`
B. velocity of propagation of the transverse wave along the string changes by `5 %`
C. velocity of propagation of the transverse wave along the string changes by `10%`.
D. fundamental wave length on the string does not change.

Answer

A, C, D

Explanation

`f prop sqrt(T)`
`(f_(2))/(f_(1)) = sqrt((T_(2))/(T_(1))) = sqrt((1.21 T_(1))/(T_(1)))`
`rArr (f_(1) + 15)/(f_(1)) = 1.1 rArr f_(1) = 150 Hz`
`(v_(2))/(v_(1)) = sqrt((T_(2))/(T_(1))) = 1.1 rArr v_(2) = 1.1 v_(1)`
So , velocity increases by `10%`. Fundamental wavelength is `lambda = 2 L`, which remains same as the length of string remains same.