# 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

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.

#### 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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