If the length of a stretched string is shortened by `40 %` and the tension is increased by `44 %`, then the ratio of the final and initial fundamental frequencies is

Options

A. `2:1`
B. `3:2`
C. `3:4`
D. `1:3`

Answer

A

Explanation

`f=(1)/(2l)sqrt((T)/(mu))impliesfpropsqrt(T)/(l)implies(f.)/(f)=sqrt((T.)/(T))xx(l)/(l.)`
Since, `T.=1.44T and l.=l-0.4l=(3)/(5)l`
`therefore (f.)/(f)=sqrt((1.44T)/(T))xx(l)/((3//5)l)=(1.25xx5)/(3)=(2)/(1)`