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The equation of a travelling wave is ...

The equation of a travelling wave is
`y(x, t) = 0.02 sin ((x)/(0.05) + (t)/(0.01)) m`
Find (a) the wave velocity and
(b) the particle velocity at `x = 0.2 m and t = 0.3 s`.
Given `cos theta = -0.85`, where `theta = 34 rad`

Text Solution

Verified by Experts

The correct Answer is:
A, B
(a) Wave velocity = ("Coefficient of t")/("Coefficient of x")`
`=(1//0.01)/(1//0.05) = 5 m//s`
Since, coefficient of `t` and coefficient pa `x` are of same sign. Hence, wave is travelling in negstive x-direction.
or `v = -5 m//s`
(b) Velocity of particle,
`v_(P) = (dely)/(delt) = 2 cos((x)/(0.05) + (t)/(0.01))`
Substituting `x=0.2` and `t=0.3`, we have
`v_(P) =2 cos(34) = 2(-0.85)`
`= -1.7 m//s`
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