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 - Physics MCQ JEE Main 2026 | ExamTest.live

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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 \times 1 0^{3} kg/m^{3} and 2.2 \times 1 0^{11} N/m^{2} respectively?

Solution & Step-by-step Explanation

1. Fundamental frequency f = \frac{1}{2 l} \frac{T}{μ} where μ = ρ A .2. f = \frac{1}{2 l} \frac{T}{ρ A} = \frac{1}{2 l} \frac{Stress}{ρ} .3. From Young's Modulus Y = \frac{Stress}{Strain} \Rightarrow Stress = Y \times Strain . Strain = 1% = 0.01 . Stress = 2.2 \times 1 0^{11} \times 0.01 = 2.2 \times 1 0^{9} N/m^{2} .4. f = \frac{1}{2 \times 1.5} \frac{2.2 \times 1 0 ^{9}}{7.7 \times 1 0 ^{3}} = \frac{1}{3} \frac{2}{7} \times 1 0^{6} = \frac{1000}{3} 0.2857 f \approx \frac{1000}{3} \times 0.5345 \approx 178.2 Hz .

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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 \times 1 0^{3} kg/m^{3} and 2.2 \times 1 0^{11} N/m^{2} respectively?

178.2 Hz

200.5 Hz

770 Hz

188.5 Hz

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