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?

Engineering

Physics

Standing Wave on String

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?

188.5 Hz

770 Hz

178.2 Hz

200.5 Hz

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$f = \frac{V}{2 ℓ} = \frac{1}{2 ℓ} \sqrt{\frac{T}{μ}}$

$\frac{T}{µ} = \frac{y}{ρ} \times \frac{Δℓ}{ℓ}$

$\Rightarrow f = \frac{1}{2 \times 1.5} \sqrt{\frac{2.2 \times 10^{11} \times 0.01}{7.7 \times 10^{3}}}$

$= \frac{1}{3} \sqrt{\frac{2}{7} \times 10^{6}}$

$= \frac{1}{3} \sqrt{\frac{2}{7}} = \times 103 = 178 .2 Hz$