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A uniform rope of mass 0.1 kg and leng...

A uniform rope of mass `0.1 kg` and length `2.45 m` hangs from a ceiling.
(a) Find the speed of transverse wave in the rope at a point `0.5 m` distant from the lower end.
(b) Calculate the time taken by a transverse wave to travel the full length of the rope.

Text Solution

Verified by Experts

(b) From Eq. (i) we see that velocity of the wave is different at different points. So, if at point x the wave travels a distance dx in time dt, then
`dt=(dx)/V=(dx)(sqrt(gx))`
`therefore int_0^tdt=int_0^l(dx)/(sqrt(gx))`
or `t=2 sqrt(l/g)=2sqrt((2.45)/(9.8)) =1.0s`
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