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 × 10¹¹N/m² respectively?

188.5 Hz

178.2 Hz

200.5 Hz

770 Hz

Solution

178.2 Hz

Fundamental space frequency space straight f space equals space fraction numerator 1 over denominator 2 l end fraction square root of straight T over straight mu end root equals space fraction numerator 1 over denominator 2 l end fraction square root of straight T over Aρ end root space equals equals space fraction numerator 1 over denominator 2 l end fraction square root of Stress over straight rho end root space equals fraction numerator 1 over denominator 2 space straight x 1.5 end fraction square root of fraction numerator 2.2 space straight x space 10 to the power of 11 space straight x space 10 to the power of negative 2 end exponent over denominator 7.7 space straight x space 10 cubed end fraction end root

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