The fundamental frequeney of a sonumeter wire of length 'l' is `f_(0)` A bridge is now introduced at a distance of `Deltal` from the centre of the wire `(Deltal lt lt l)` . Find the number of beats heard if both sides of the bridge are set into vibration in their fundamental modes.

Explanation

`f_(0)=(v)/(2l)`, now beat frequency `f=f_(1)-f_(2)`
`=(v)/(2)[(1)/(((l)/(2)-Deltal))-(1)/(((l)/(2)+Deltal))]`

`=(f_(0)l)[(2)/((l-Deltal))-(2)/((l+2Deltal))]`
`=(2f_(0)l)[(l+2Deltal-l+2Deltal)/(l^(2)-4(Deltal)^(2))]~~(8f_(0)Deltal)/(l)`