(B) In the condition of resonance,the frequency of the alternating current $(n)$ is equal to the fundamental frequency of the vibrating wire.The funda

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(B) In the condition of resonance,the frequency of the alternating current $(n)$ is equal to the fundamental frequency of the vibrating wire.The fundamental frequency of a stretched string is given by $n = \frac{1}{2l} \sqrt{\frac{T}{\mu}}$,where $l$ is the length,$T$ is the tension,and $\mu$ is the linear mass density.Given:Length $l = 1 \, m$Tension $T = 10 \, kg \text{-} wt = 10 \times 9.8 \, N = 98 \, N$Linear mass density $\mu = 9.8 \, g/m = 9.8 \times 10^{-3} \, kg/m$Substituting the values:$n = \frac{1}{2 \times 1} \sqrt{\frac{98}{9.8 \times 10^{-3}}}$$n = \frac{1}{2} \sqrt{10000}$$n = \frac{1}{2} \times 100 = 50 \, Hz$.

Class 11 Physics Waves and Sound Transverse Stationary Waves and Sonometer

Medium

$A$ metal wire of linear mass density of $9.8 \, g/m$ is stretched with a tension of $10 \, kg$ weight between two rigid supports $1 \, m$ apart. The wire passes at its middle point between the poles of a permanent magnet,and it vibrates in resonance when carrying an alternating current of frequency $n$. The frequency $n$ of the alternating source is ..... $Hz$.

AIEEE 2003 All AIEEE

A
$25$
B
$50$
C
$100$
D
$200$

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Waves and Sound

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Transverse Stationary Waves and Sonometer

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$A$ steel wire is used to stretch a spring. An oscillating magnetic field drives the steel wire up and down. $A$ standing wave with three antinodes is created when the spring is stretched by $4.0\, cm$. What stretch of the spring produces a standing wave with two antinodes with the same frequency (in $, cm$)?

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Two uniform strings $A$ and $B$ made of steel are made to vibrate under the same tension. If the first overtone of $A$ is equal to the second overtone of $B$ and if the radius of $A$ is twice that of $B$, the ratio of the lengths of the strings is :

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$A$ steel rod $100 \ cm$ long is clamped at its mid-point. The fundamental frequency of longitudinal vibrations of the rod is given to be $2.53 \ kHz$. What is the speed of sound in steel in $km/s$ (in $.06$)?

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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 $\,Hz$)

EasyAP EAMCET 2012

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$A$ tuning fork gives $4$ beats with $50 \ cm$ length of a sonometer wire. If the length of the wire is shortened by $1 \ cm$,the number of beats is still the same. The frequency of the fork is (in $Hz$)

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Two uniform strings $A$ and $B$ made of steel are made to vibrate under the same tension. If the first overtone of $A$ is equal to the second overtone of $B$ and if the radius of $A$ is twice that of $B$, the ratio of the lengths of the strings is :

$A$ steel rod $100 \ cm$ long is clamped at its mid-point. The fundamental frequency of longitudinal vibrations of the rod is given to be $2.53 \ kHz$. What is the speed of sound in steel in $km/s$ (in $.06$)?

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 $\,Hz$)

$A$ tuning fork gives $4$ beats with $50 \ cm$ length of a sonometer wire. If the length of the wire is shortened by $1 \ cm$,the number of beats is still the same. The frequency of the fork is (in $Hz$)

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