Numerical

A sonometer wire is in unison with a tuning fork of frequency 125 Hz when it is stretched by a weight. When the weight is completely immersed in water, 8 beats are heard per second. Find the specific gravity of the material of the weight.

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#### Solution

n_{1} = 125 Hz, n_{2} = n_{1} - 8 = 125 - 8 = 117 Hz

As,

`n_1/n_2 = sqrt("P"/"P - 1")`

`125/117 = sqrt("P"/"P - 1")`

`1.068 = sqrt("P"/"P - 1")`

⇒ P = 1.141P - 1.141

1.141 = 1.141P - P

P = `[1.141]/[0.141]`

∴ P = 8.09

Concept: Formation of Beats

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