If the length of a stretched string is shortened by x% and the tension is increased by 44%. Then the ratio of the final and initial fundamental frequencies is `2:1`, then the value of x is

Options

A. 20
B. 30
C. 40
D. 60

Answer

C

Explanation

Fundamental frequency for string, `n = (1)/(2l) sqrt((T)/(m))`
So, `n prop sqrtT//l`
`rArr (n.)/(n) = sqrt((T.)/(T)) xx (l)/(l.)` …(i)
Now, `T. = T + 0.44T = (144T)/(100)`
and `l. = l - (x)/(100) l = ((100 - x)/(100)) l`
Also, `(n.)/(n) = (2)/(1)`
`(2)/(1) = sqrt((144T)/(100T)) xx (l)/(((100 -x)/(100))l) = (12)/(10) xx (100)/(100 -x)`
or `(100-x) = 60 or x = 40`