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`.

Answer

A, B

Explanation

(a) Wave velocity `= ("Coefficient of t")/("Coefficient of x")`
`=((1//0.01))/((1//0.05)) = 5 m//s`
Since, coefficient of `t` and coefficient of `x` are of same sign. Wave is travelling in negative x-direction.
or `v= - 5m//s`
(b) Particle velocity, `v_(P) = (dely)/(delt)`
`=2 cos ((x)/(0.05) + (t)/(0.01))`
Substituting `x = 0.2` and
`t = 0.3`, we have
`= (2)(-0.85)`
`= - 1.7 m//s`