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A taut string having tension 100 N and l...

A taut string having tension 100 N and linear mass density `0.25 kg//m` is used inside a cart to generate a wave pulse starting at the left end, as shown. What should be the velocity of the cart so that pulse remains stationary w.r.t. ground.

Text Solution

Verified by Experts

The expression `v=sqrt(T)/(mu)` gives the velocity of the wave in the string. Here the string is moving with cart.
velocity of pulse `v=sqrt(T//mu)=20m//s`
This velocity is w.r.t. car.
Velocity of the pulse can be given as
Now `vec(v)_(P)=vec(v)_(PC)+vec(v)(CG)`
`0=20i+vec(v)_(CG)`
`vec(v)_(CG)=-20i m//s`
Hence, the cart should move with velocity `20 m//s` in the direction opposite to the pulse.
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