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A uniform rope of mass m and length L ha...

A uniform rope of mass m and length L hangs from a ceiling. (a) Show that the speed of a transverse wave on the rope is a function of y, the distance from the lower end, and is given by `v=sqrt(gy)`. (b) Show that the time a transverse wave takes to travel the length of the rope is given by `t=2 sqrt(L//g)`.

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A uniform rope of mass m and length L hangs from a celling. (a) Show that the speed of a transverse wave on the rope is a function of y , the distance from the lower end, and is given by t = 2sqrt(L//g) .

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Knowledge Check

  • A uniform rope of mass 0.1 kg and length 2.5 m hangs from ceiling. The speed of transverse wave in the rope at upper end at a point 0.5 m distance from lower end will be

    A
    `5" ms"^(-1) and 2.24 "ms"^(-1)`
    B
    `10" ms"^(-1) and 3.23 "ms"^(-1)`
    C
    `7.5" ms"^(-1) and 1.2 "ms"^(-1)`
    D
    None of these

  • A uniform rope of mass M=0.1kg and length L=10m hangs from the celling. [g=10m//s^(2)] :-

    A
    Speed of the transverse wave in the rope increases linearly from top to the bottom
    B
    Speed of the transverse wave in the rope decreases linearly from bottom to the top
    C
    Speed of the transverse wave in the rop ramain constant along the length of the rope
    D
    Time taken by the transverse wave to travel the full length of the rope is 2 sec

  • A string of length L and mass M hangs freely from a fixed point. Then the velocity of transverse waves along the string at a distance x from the free end is

    A
    `sqrt(gL)`
    B
    `sqrt(gx)`
    C
    gL
    D
    gx

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