(B) The velocity of a transverse wave in a stretched string is given by $v = \sqrt{\frac{T}{\mu}}$,where $T$ is the tension and $\mu$ is the linear ma

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(B) The velocity of a transverse wave in a stretched string is given by $v = \sqrt{\frac{T}{\mu}}$,where $T$ is the tension and $\mu$ is the linear mass density.Linear mass density $\mu = \rho A = \rho (\pi R^2)$,where $\rho$ is the density of the material and $R$ is the radius of the cross section.Since both strings are made of the same material,$\rho$ is constant. Given that the tension $T$ is the same for both strings,we have $v \propto \frac{1}{\sqrt{R^2}} \propto \frac{1}{R}$.Therefore,$\frac{v_2}{v_1} = \frac{R_1}{R_2}$.Given $R_1 = R$ and $R_2 = R/2$,we get $\frac{v_2}{v_1} = \frac{R}{R/2} = 2$.

Class 11 Physics Waves and Sound Speed of Mechanical Wave on String (Transverse wave)

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Two strings with circular cross section and made of same material are stretched to have the same amount of tension. $A$ transverse wave is then made to pass through both the strings. The velocity of the wave in the first string having the radius of cross section $R$ is $v_1$,and that in the other string having radius of cross section $R/2$ is $v_2$. Then $\frac{v_2}{v_1} = $

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A
$\sqrt{2}$
B
$2$
C
$8$
D
$4$

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Speed of Mechanical Wave on String (Transverse wave)

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$A$ string of mass $0.1 \, kg$ is under a tension $1.6 \, N$. The length of the string is $1 \, m$. $A$ transverse wave starts from one end of the string. The time taken by the wave to reach the other end is (in $s$.)

MediumMHT CET 2020

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$A$ steel wire with mass per unit length $7.0 \times 10^{-3} \, kg \, m^{-1}$ is under tension of $70 \, N$. The speed of transverse waves in the wire will be $......... \, m/s$.

EasyJEE MAIN 2023

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The mass per unit length of a uniform wire is $0.135 \, g/cm$. $A$ transverse wave of the form $y = -0.21 \sin(x + 30t)$ is produced in it,where $x$ is in meters and $t$ is in seconds. Then,the expected value of tension in the wire is $x \times 10^{-2} \, N$. The value of $x$ is (Round off to the nearest integer).

DifficultJEE MAIN 2021

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$A$ uniform string of length $20 \ m$ is suspended from a rigid support. $A$ short wave pulse is introduced at its lowest end. It starts moving up the string. The time taken to reach the support is (take $g = 10 \ ms^{-2}$):

DifficultJEE MAIN 2016

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$A$ uniform rope of mass $0.1 \,kg$ and length $2.45 \,m$ hangs from a rigid support. The time taken by a transverse wave formed in the rope to travel through the full length of the rope is (Assume $g = 9.8 \,m/s^2$). (in $\,s$)

DifficultAP EAMCET 2012

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$A$ string of mass $0.1 \, kg$ is under a tension $1.6 \, N$. The length of the string is $1 \, m$. $A$ transverse wave starts from one end of the string. The time taken by the wave to reach the other end is (in $s$.)

$A$ steel wire with mass per unit length $7.0 \times 10^{-3} \, kg \, m^{-1}$ is under tension of $70 \, N$. The speed of transverse waves in the wire will be $......... \, m/s$.

$A$ uniform string of length $20 \ m$ is suspended from a rigid support. $A$ short wave pulse is introduced at its lowest end. It starts moving up the string. The time taken to reach the support is (take $g = 10 \ ms^{-2}$):

$A$ uniform rope of mass $0.1 \,kg$ and length $2.45 \,m$ hangs from a rigid support. The time taken by a transverse wave formed in the rope to travel through the full length of the rope is (Assume $g = 9.8 \,m/s^2$). (in $\,s$)

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