(D) The frequency of a vibrating string is given by $f = \frac{p}{2L} \sqrt{\frac{T}{\mu}}$, where $p$ is the number of loops (antinodes), $L$ is the

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(D) The frequency of a vibrating string is given by $f = \frac{p}{2L} \sqrt{\frac{T}{\mu}}$, where $p$ is the number of loops (antinodes), $L$ is the length, $T$ is the tension, and $\mu$ is the linear mass density.Since the tuning fork frequency $f$ and length $L$ remain constant, we have $p \propto \sqrt{T}$, or $T \propto p^2$.Therefore, $T_1 p_1^2 = T_2 p_2^2$.Given $T_1 = 9 \,kg-wt$, $p_1 = 5$, and $p_2 = 3$.Substituting the values: $9 \times 5^2 = M \times 3^2$.$9 \times 25 = M \times 9$.$M = 25 \,kg$.

Class 11 Physics Waves and Sound Transverse Stationary Waves and Sonometer

Medium

$A$ sonometer wire resonates with a given tuning fork forming standing waves with five antinodes between the two bridges when a mass of $9 \,kg$ 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

MHT CET 2021 All MHT CET

A
$5 \,kg$
B
$12.5 \,kg$
C
$\frac{1}{25} \,kg$
D
$25 \,kg$

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Waves and Sound

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Transverse Stationary Waves and Sonometer

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