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Question

A uniform rope of mass 0.1 kg and length 2.45 m hangs from a ceiling. The time taken by a transverse wave to travel through the full length of the rope is
[Take g=9.8 m/s2]

A
2.0 s
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B
1.2 s
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C
1.0 s
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D
2.2 s
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Solution

The correct option is C 1.0 s
Let M be the total mass of the rope and L be its length.


Tension at distance x from the bottom is given by
T=(MLx)g

Velocity of wave at distance x, v=Tμ=    (MxL)gML=gx

v=dxdt=gx or dt=dxgx
Integrating from x=0 to L,
t=1gL0x12dx
or t=2Lg=22.459.8=1 s

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