A uniform rope of mass 0.1kg and length 2.45m hangs from a ceiling. The time taken by a transverse wave to travel through the full length of the rope is
[Take g=9.8m/s2]
A
2.0s
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B
1.2s
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C
1.0s
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D
2.2s
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Solution
The correct option is C1.0s
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=dx√gx
Integrating from x=0 to L, t=1√gL∫0x−12dx
or t=2√Lg=2√2.459.8=1s