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The equation for a wave travelling in x-...

The equation for a wave travelling in x-direction 0n a string is
`y = (3.0 cm) sin [(3.14 cm^(-1) x -(314 s^(-1)t]`
(a) Find the maximum velocity of a particle of the string.
(b) Find the acceleration of a particle at `x = 6.0 cm` at time `t = 0.11 s`

Text Solution

Verified by Experts

The correct Answer is:
A, B, D
(a) The velocity of the particle at `x`at time `t` is
`v =(dely)/(delt) = (3.0 cm) (-314 s^(-1)) cos [(3.14 cm^(-1)) x - (314 s^(-1)t]`
`=(-9.4 ms^(-1)) cos [(3.14 cm ^(-1)) x - (314 s^(-1))t]`
The maximum velocity of a particle will be
` v = 9.4 ms^(-1)`
(b) The acceleration of the particle at `x`at time `t` is
`a = (delv)/(delt) = -(9.4 ms^(-1))(314 s^(-1)) sin[(3.14 cm^(-1)) x - (314 s^(-1))t]`
`= -(2952 ms^(-1)sin[(3.14 cm^(-1)) x - (314 s^(-1))t]`
The acceleration of the particle at `x = 6.0 cm` at time `t = 0.11 s`is
`a =-(2952 ms^(-2))sin[(6pi - 11pi)] = 0`
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