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

`l_(2)=l_(1)-(40)/(100)l_(1)=(60)/(100)l_(1)=0.6l_(1)`
`T_(2)=T_(1)+(44)/(100)T_(1)=1.44T_(1)` and `(n_(2))/(n_(1))=(l_(1))/(l_(2))sqrt((T_(2))/(T_(1)))`