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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. - Physics

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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

n1 = 125 Hz, n2 = n1 - 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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