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MHT CET 2024 (9 May, Shift 1) · Stationary Waves & Vibrating Strings

Stationary Waves & Vibrating Strings question from MHT CET 2024 (9 May, Shift 1)

Q54MHT CET 2024 · 9 MAY · SHIFT 1Medium

Stationary Waves & Vibrating Strings

A sonometer wire is stretched by hanging a metal bob, the fundamental frequency of the wire is ' $n_1$ '. When the bob is completely immersed in water, the frequency of vibration of wire becomes ' $n_2$ '. The relative density of the metal of the bob is

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Answer: (c)

$n \propto \sqrt{T}$ ; $T_1 = V\rho g$ in air, $T_2 = V(\rho - \rho_w)g$ in water.
$\dfrac{n_2^2}{n_1^2} = \dfrac{d-1}{d} \Rightarrow d = \dfrac{n_1^2}{n_1^2 - n_2^2}$
So the answer is (c).

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