(B) The frequency of a vibrating wire is given by $n = \frac{1}{2l} \sqrt{\frac{T}{\mu}}$. Since tension $T$ and mass per unit length $\mu$ are consta

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(B) The frequency of a vibrating wire is given by $n = \frac{1}{2l} \sqrt{\frac{T}{\mu}}$. Since tension $T$ and mass per unit length $\mu$ are constant,we have $n \propto \frac{1}{l}$,which implies $nl = \text{constant}$.Let $n$ be the frequency of the tuning fork.At length $l_1 = 100 \,cm$,the frequency of the wire is $n_1 = n + 8$ (since beats are heard).At length $l_2 = 101 \,cm$,the frequency of the wire is $n_2 = n - 8$ (as frequency decreases with increasing length).Using $n_1 l_1 = n_2 l_2$:$(n + 8) \times 100 = (n - 8) \times 101$$100n + 800 = 101n - 808$$101n - 100n = 800 + 808$$n = 1608 \,Hz$.

Class 11 Physics Waves and Sound 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 $\,Hz$)

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A
$1616$
B
$1608$
C
$1632$
D
$1600$

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Waves and Sound

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Transverse Stationary Waves and Sonometer

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The frequency of a sonometer wire is $100 \ Hz$. When the weights producing the tension are completely immersed in water,the frequency becomes $80 \ Hz$,and on immersing the weights in a certain liquid,the frequency becomes $60 \ Hz$. The specific gravity of the liquid is:

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MediumJEE MAIN 2013

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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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Two strings $A$ and $B$ of lengths $L_A = 80 \text{ cm}$ and $L_B = x \text{ cm}$ respectively are used separately in a sonometer. The ratio of their densities $(d_A / d_B)$ is $0.81$. The diameter of $B$ is one-half that of $A$. If the strings have the same tension and fundamental frequency,the value of $x$ is:

DifficultTS EAMCET 2006

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Two wires made up of the same material are of equal lengths but their radii are in the ratio $1 : 2$. On stretching each of these two strings by the same tension,the ratio between the fundamental frequencies is

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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 $\,Hz$)

Similar Questions

The frequency of a sonometer wire is $100 \ Hz$. When the weights producing the tension are completely immersed in water,the frequency becomes $80 \ Hz$,and on immersing the weights in a certain liquid,the frequency becomes $60 \ Hz$. The specific gravity of the liquid is:

$A$ sonometer wire of length $1.5 \ m$ is made of steel. The tension in it produces an elastic strain of $1 \%$. What is the fundamental frequency of steel if density and elasticity of steel are $7.7 \times 10^3 \ kg/m^3$ and $2.2 \times 10^{11} \ N/m^2$ respectively (in $Hz$)?

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 $kg \ wt$)

Two wires made up of the same material are of equal lengths but their radii are in the ratio $1 : 2$. On stretching each of these two strings by the same tension,the ratio between the fundamental frequencies is

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