The fundatmental frequency of a sonometer wire increases by `6 Hz` if its tension is increased by `44%` keeping the length constant. Find the change in the fundamental frequency of the sonometer when the length of the wire is increased by `20%` keeping the original tension in the wire.

Answer

Decrease by `5Hz`

Explanation

`f = (1)/(2L) sqrt((T)/(mu))`
If length is constant
`(f')/(f) = ((T')/(T))^(1/2)`
`f' = f + 6, T' = T + 0.44 T = 1.44 T`
`(f + 6)/(f) = sqrt((1.44T)/(T))`
`f = 30Hz`
It `T` is constant
`(f")/(f) = (l)/(1.20l)`
`f" = (f)/(1.2) = (300)/(12)`
`f" = 25Hz`
`Deltaf = f" - f = 25 - 30 = -5 Hz`
So fundamental freq. Will decreases by `5Hz`