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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?
- 188.5 Hz
- 178.2 Hz
- 200.5 Hz
- 770 Hz
Correct answer: 178.2 Hz
Solution
The fundamental frequency of a vibrating wire can be calculated using the formula that incorporates the tension, length, density, and elasticity of the material. Given the parameters for the steel wire and the specified elastic strain, the calculations yield a fundamental frequency of 178.2 Hz, confirming option B as the correct answer.
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