The fundamental frequency of a wire of certain length is 400 Hz. When the length of the wire is decreased by 10 cm, without changing the tension in the wire, the frequency becomes 500 Hz. What was the original length of 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`