A sonometer wire resonates with a given tuning fork forming standing… | MHT CET 2021 (22 Sep, Shift 1)

Q78MHT CET 2021 · 22 SEP · SHIFT 1Medium

Stationary Waves & Vibrating Strings

A sonometer wire resonates with a given tuning fork forming standing waves with five antinodes between the two bridges when a mass of $9\text{ kg}$ is suspended from the wire. When this mass is replaced by a mass $M$ , the wire resonates with the same tuning fork forming three antinodes for the same positions of the bridges. The value of ' $M$ ' is

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Answer: (d)

Same fork and same bridge length: $n=\frac{p}{2L}\sqrt{\frac{T}{\mu}}$ , so $p\sqrt{T}=$ constant ( $p$ = number of loops = antinodes).
$5\sqrt{9g}=3\sqrt{Mg} \Rightarrow \sqrt{M}=5$
So the answer is (d) $25\text{ kg}$ .

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