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Derive an expression for the velocity of...

Derive an expression for the velocity of pulse in a in stretched in string under a tension `T` and `mu` is the mass per unit length of the sting.

Text Solution

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The correct Answer is:
The broad view of the pulse under the tension `T` is given by
`(##RES_WFPM_PHY_XI_C05_E01_014_A01##)`
As; `2T sin (theta)/(2) = dm (v^(2))/(R)`
`rArr 2T(theta)/(2) = ((m)/(l)). Rtheta (v^2))/(R)`
`rArr v = sqrt((T)/(mu))`
where `mu = (m)/(l)`, is the mass per unit length of the string also known as the linear mass density.
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Knowledge Check

  • The speed on string with tension T and linear mass density mu is -

    A
    `V = sqrt(T/mu)`
    B
    `V = sqrt(B/rho)`
    C
    `V = sqrt(Y/rho)`
    D
    None of these

  • The velocity of transverse wave in a string is v = sqrt( T//m) where T is the tension in the string and m is the mass per unit length . If T = 3.0 kgf , the mass of string is v = 1.000 m , then the percentage error in the measurement of velocity is

    A
    `0.5`
    B
    `0.7`
    C
    `2.3`
    D
    `3.6`

  • The successive resonating frequencies for a stretched wire are 250 Hz and 300 Hz. The wire is stretched between two rigid supports with a tension of 36 N. If the mass per unit length of the wire is 0.01 kg, then the length of the wire is

    A
    40 cm
    B
    50 cm
    C
    60 cm
    D
    70 cm

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