A wire of length ' L ', diameter ' d ', density of material ' ρ ' is… | MHT CET 2026 (20 Apr, Shift 1)

Q19MHT CET 2026 · 20 APR · SHIFT 1Medium

Stationary Waves & Vibrating Strings

A wire of length ' $L$ ', diameter ' $d$ ', density of material ' $\rho$ ' is under tension ' $T$ ' has fundamental frequency of vibration ' $n_A$ '. Another wire of length ' $2L$ ', diameter ' $3d$ ', density of material ' $2\rho$ ' is vibrated under tension ' $2T$ ', the fundamental frequency of vibration becomes ' $n_B$ '. The ratio $n_B : n_A$ is

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Answer: (c)

$n = \dfrac{1}{Ld}\sqrt{\dfrac{T}{\pi\rho}} \Rightarrow n \propto \dfrac{1}{Ld}\sqrt{\dfrac{T}{\rho}}$
$\dfrac{n_B}{n_A} = \dfrac{L \cdot d}{2L \cdot 3d}\sqrt{\dfrac{2T/2\rho}{T/\rho}} = \dfrac{1}{6}$
So the answer is (c) $1:6$ .

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Stationary Waves & Vibrating Strings question from MHT CET 2026 (20 Apr, Shift 1)

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