A string is stretched so that its length is increased by `1/eta` of its original length. The ratio of fundamental frequency of transverse vibration to that of fundamental frequency of longitudinal vibration will be

Options

A. ` 1: n`
B. ` n^(2) : 1`
C. `sqrt(n) : 1`
D. `n : 1`

Answer

C

Explanation

Velocity of longitudinal waves
`v_(1) = sqrt((Y)/( rho))`
and velocity of tranverse waves
`v_(2) = sqrt((T)/(m)) = sqrt ((T)/(rho s))`
`:. (v_(1))/(v_(2)) = sqrt((y)/( T//s)) = sqrt((Y)/( Y (( Delta l)/(l)))) = sqrt (n)`
`[ because Delta l = (l)/(n) ]`
Now `f prop v`
`:. (f_(1))/( f_(2)) = (v_(1))/(v_(2)) = sqrt(n)`
In the above frequency , `rho =` density of string , `s =` area of cross - section of string , `Y =` Young's modulus.