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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 × 10³ kg/m³ and 2.2 × 10¹¹ N/m² respectively ?

1. 200.5 Hz
2. 770 Hz
3. 188.5 Hz
4. 178.2 Hz

Correct answer: 178.2 Hz

Solution

The fundamental frequency of a vibrating string is determined by its length, tension, and mass per unit length. Given the elastic properties and density of steel, the calculations yield a frequency of 178.2 Hz, which aligns with the physical principles governing the vibration of strings under tension.

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