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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
770 Hz
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D
200.5 Hz
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Solution

## The correct option is B 178.2 HzFrequency, f=v2l=12l√Tμ=12l√TAρ Where, T= tension in the wire and μ= mass per unit length of wire Also, Young's modulus, Y=TlAΔl ⇒TA=YΔll Putting the value in expression of frequency, f=12l√YΔlld .......(1) Given:l=1.5 m,Δll=0.01, ρ=7.7×103 kg/m3 and y=2.2×1011 N/m2 On putting these values in eq. (1), f=12l√2.2×1011×0.017.7×103 f=1033√27 f≈178.2 Hz Hence, option (B) is correct.

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