(A) The tension $T$ in the wire is provided by the spring: $T = kx = 50 \ N/m \times 0.01 \ m = 0.5 \ N$. The mass per unit length $\mu$ of the wire i

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(A) The tension $T$ in the wire is provided by the spring: $T = kx = 50 \ N/m \times 0.01 \ m = 0.5 \ N$. The mass per unit length $\mu$ of the wire is calculated as: $\mu = \frac{m}{l} = \frac{10 \times 10^{-3} \ kg}{0.5 \ m} = 0.02 \ kg/m$. The speed $v$ of the wave pulse on the string is given by: $v = \sqrt{\frac{T}{\mu}} = \sqrt{\frac{0.5}{0.02}} = \sqrt{25} = 5 \ m/s$. The time $t$ taken by the pulse to travel the length of the wire is: $t = \frac{l}{v} = \frac{0.5 \ m}{5 \ m/s} = 0.1 \ s$.

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

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$A$ wire of length $50 \ cm$ and weighing $10 \ g$ is attached to a spring at one end and to a fixed wall at the other end. The spring has a spring constant of $50 \ N/m$ and is stretched by $1 \ cm$. If a wave pulse is produced on the string near the wall,then how much time will it take to reach the spring (in $s$)?

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$0.1$
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$0.2$
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$0.4$

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Waves and Sound

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Speed of Mechanical Wave on String (Transverse wave)

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$A$ string has a mass per unit length of $10^{-6} \,kg/cm$. The equation of a simple harmonic wave produced in it is $Y=0.2 \sin(2x+80t) \,m$. The tension in the string is: (in $N$)

DifficultMHT CET 2024

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$Assertion :$ Two waves moving in a uniform string having uniform tension cannot have different velocities.
$Reason :$ Elastic and inertial properties of string are same for all waves in same string. Moreover,the speed of a wave in a string depends on its elastic and inertial properties only.

EasyAIIMS 2015

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Transverse waves of the same frequency are generated in two steel wires $A$ and $B$. The diameter of $A$ is twice that of $B$,and the tension in $A$ is half that in $B$. The ratio of the velocities of the waves in $A$ and $B$ is:

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When the area of cross-section of a stretched wire is halved and tension is doubled,the speed of propagation of transverse waves along it becomes $k$ times the initial speed. Then,$k$ is:

MediumAP EAMCET 2020

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$A$ transverse wave propagating on a stretched string of linear density $3 \times 10^{-4} \ kg \ m^{-1}$ is represented by the equation $y = 0.2 \sin (1.5 x + 60 t)$,where $x$ is in metres and $t$ is in seconds. The tension in the string (in newton) is

DifficultAP EAMCET 2005

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$A$ string has a mass per unit length of $10^{-6} \,kg/cm$. The equation of a simple harmonic wave produced in it is $Y=0.2 \sin(2x+80t) \,m$. The tension in the string is: (in $N$)

$Assertion :$ Two waves moving in a uniform string having uniform tension cannot have different velocities.$Reason :$ Elastic and inertial properties of string are same for all waves in same string. Moreover,the speed of a wave in a string depends on its elastic and inertial properties only.

Transverse waves of the same frequency are generated in two steel wires $A$ and $B$. The diameter of $A$ is twice that of $B$,and the tension in $A$ is half that in $B$. The ratio of the velocities of the waves in $A$ and $B$ is:

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$Assertion :$ Two waves moving in a uniform string having uniform tension cannot have different velocities.
$Reason :$ Elastic and inertial properties of string are same for all waves in same string. Moreover,the speed of a wave in a string depends on its elastic and inertial properties only.