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MHT CET 2023 (11 May, Shift 2) · Stationary Waves & Vibrating Strings

Stationary Waves & Vibrating Strings question from MHT CET 2023 (11 May, Shift 2)

Q66MHT CET 2023 · 11 MAY · SHIFT 2Medium

Stationary Waves & Vibrating Strings

A sonometer wire ' $A$ ' of diameter ' $d$ ' under tension ' $T$ ' having density ' $\rho_1$ ' vibrates with fundamental frequency ' $n$ '. If we use another wire ' $B$ ' which vibrates with same frequency under tension ' $2T$ ' and diameter ' $2d$ ' then density ' $\rho_2$ ' of wire ' $B$ ' will be

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Answer: (c)

Same length: $n \propto \dfrac{1}{d}\sqrt{\dfrac{T}{\rho}}$ .
$\dfrac{1}{d}\sqrt{\dfrac{T}{\rho_1}} = \dfrac{1}{2d}\sqrt{\dfrac{2T}{\rho_2}} \Rightarrow \dfrac{1}{\rho_1} = \dfrac{2}{4\rho_2}$
$\rho_2 = \dfrac{\rho_1}{2}$
So the answer is (c) $\rho_2 = \dfrac{\rho_1}{2}$ .

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