A sonometer wire of length 1.5m 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 7.7×103kg/m3 and 2.2×1011N/m2, respectively?
A
188.5Hz
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B
178.2Hz
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C
250.5Hz
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D
770Hz
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Solution
The correct option is B178.2Hz Given:
Length of wire, l=1.5m
Elastic strain, Δll=1%=0.01
Density, ρ=7.7×103kg/m3
Elasticity of steel, Y=2.2×1011N/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=12l√Tμ=12l√TρA.....(1)
Also, Young's modulus, Y=T/AΔl/l ⇒TA=YΔll........(2)
From Eq. (1) and (2), f=12l√YΔlρl =12×1.5√2.2×1011×0.017.7×103=178.2Hz
Hence, option (b) is true.