In order to double the frequency of the fundamental note emitted by a streched string, the length is reduced to `3/4th` of the original length and the tension is chaged. The factor by which the tension is to be changed is

Options

A. `3/8`
B. `2/3`
C. `8/9`
D. `9/4`

Answer

D

Explanation

Frequency of strectched string `n=1/(2l)sqrt(T/m)`
`n propsqrtT/l`
`n_1/n_2=l_1/l_2sqrt(T_1/T_2)`
Frequency doubled and length reduced to `3/4` then
`implies n_2=2n_1,l_2=3/4l_1`
`implies n_2/(2n_1)=(3/4(l_1))/l_1=sqrt(T_1/T_2)`
`T_1/T_2=4/9`
`T_2=4/9T_1`