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

Answer

B

Explanation

Fundamental frequency, `upsilon=(1)/(2l)sqrt((T)/(mu))`
`therefore (upsilon_(2))/(upsilon_(1))=(l_(1))/(l_(2))sqrt((T_(2))/(T_(1)))=(l_(1))/((l_(1)-(40)/(100)l_(1)))sqrt(((T_(1)+(44)/(100)T_(1))/(T_(1))))`
or `(upsilon_(2))/(upsilon_(1))=(100)/(60)xx(12)/(10)=(2)/(1)or upsilon_(2):upsilon_(1)::2:1`