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## A sonometer wire of length 1.5 m is made of steel. The tension in it produce 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 ? - physics 2013

(1) 188.5 Hz

(2) 178.2 Hz

(3) 200.5 Hz

(4) 770 Hz

By:milan-ransingh

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## Answers

Transverse waves on a Sonometer wire/bridge . Young's modulus Y = Stress / Strain = 2.2 * 10^11 N/m² Stress = Tension / Cross section area = T / A Strain = 1 % = 0.01 2.2 * 10^11 = (T / A ) / 0.01 = T / (0.01 A) T = 2.2 * 10^9 * A Newtons L = 1.5 meter Volume density d = 7.7 * 10³ kg/m³ Linear density μ = volume density * Area = d * A = 7.7 * 10³ * A kg /meter velocity of transverse wave on the Sonometer wire = √(T/μ) v = √(2.2*10^9 / 7.7*10³) m/sec = 534.52 m/sec Fundamental note has a wavelength = λ = 2 * L = 3 meters. As the given wire vibrates with one loop. Nodes at both ends and anti-node at the center. So half of the wavelength is equal to the length of the wire.

So frequency = v / λ = 178.17 Hz

**(2) 178.2 Hz**

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satyashiromani

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