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the fundamental frequency of a sonometer...

the fundamental frequency of a sonometer wire of length is `f_(0)`.A bridge is now introduced at a distance of `Deltal`from the centre of the wire `(Deltal lt lt l )`. The number of beats heard if their fundamental mode are

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`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)`
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