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Question

A sonometer wire of length 1.5 m is made of steel. The tension in it produces an elastic strain of 1%. What is the fundamental frequency of steel, if density and elasticity of steel are 7.7×103 kg/m3 and 2.2×1011 N/m2, respectively?

A
188.5 Hz
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B
178.2 Hz
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C
250.5 Hz
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D
770 Hz
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Solution

The correct option is B 178.2 Hz
Given:
Length of wire, l=1.5 m
Elastic strain, Δll=1%=0.01
Density, ρ=7.7×103 kg/m3
Elasticity of steel, Y=2.2×1011 N/m2

Let T be the tension in the wire and A be the cross-sectional area.

Fundamental frequency of a sonometer wire is given by
f=12lTμ=12lTρA .....(1)
Also, Young's modulus,
Y=T/AΔl/l
TA=YΔll ........(2)

From Eq. (1) and (2),
f=12lYΔlρl
=12×1.52.2×1011×0.017.7×103=178.2 Hz
Hence, option (b) is true.

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