(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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When a vibrating tuning fork is placed on a sound box of a sonometer, $8$ beats per second are heard when the length of the sonometer wire is kept at $101 \,cm$ or $100 \,cm$. Then the frequency of the tuning fork is (Consider that the tension in the wire is kept constant). (in $\,Hz$)

EasyTS EAMCET 2012

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$A$ string of length $1 \,m$ and mass $2 \times 10^{-5} \,kg$ is under tension $T$. When the string vibrates, two successive harmonics are found to occur at frequencies $750 \,Hz$ and $1000 \,Hz$. The value of tension $T$ is . . . . . . Newton.

MediumIIT 2023

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When the tension in a string is increased by $3 \ kg \ wt$,the frequency of the fundamental mode increases in the ratio $2:3$. The initial tension in the string is: (in $kg \ wt$)

MediumMHT CET 2024

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$A$ steel wire of length $1 \ m$ and mass $0.1 \ kg$ and having a uniform cross-sectional area of $10^{-6} \ m^2$ is rigidly fixed at both ends. The temperature of the wire is lowered by $20^{\circ} C$. If the wire is vibrating in its fundamental mode,find the frequency (in $Hz$).
$(Y_{\text{steel}} = 2 \times 10^{11} \ N/m^2, \alpha_{\text{steel}} = 1.21 \times 10^{-5} /^{\circ} C)$

Difficult

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An iron load of $2 \ kg$ is suspended in air from the free end of a sonometer wire of length $1 \ m$. $A$ tuning fork of frequency $256 \ Hz$ is in resonance with $\frac{1}{\sqrt{7}}$ times the length of the sonometer wire. If the load is immersed in water, the length of the wire in metres that will be in resonance with the same tuning fork is (Specific gravity of iron $= 8$).

DifficultTS EAMCET 2004

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When a vibrating tuning fork is placed on a sound box of a sonometer, $8$ beats per second are heard when the length of the sonometer wire is kept at $101 \,cm$ or $100 \,cm$. Then the frequency of the tuning fork is (Consider that the tension in the wire is kept constant). (in $\,Hz$)

$A$ string of length $1 \,m$ and mass $2 \times 10^{-5} \,kg$ is under tension $T$. When the string vibrates, two successive harmonics are found to occur at frequencies $750 \,Hz$ and $1000 \,Hz$. The value of tension $T$ is . . . . . . Newton.

When the tension in a string is increased by $3 \ kg \ wt$,the frequency of the fundamental mode increases in the ratio $2:3$. The initial tension in the string is: (in $kg \ wt$)

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