Question

A plane progressive wave is given by `x=(40 cm) cos(50pit-0.02piy)` where `y` is in cm and `t` in `s`. The particle velocity at `y=25m` in time `t=(1)/(100)s` will be `10pisqrt(n) m//s`. What is the value of `n`.

Answer 1

Given that
`x=40 cos (50pit-0.02piy)`
:. Particle velocity
`v_(p)=(dx)/(dt)=(40xx50pi){-sin(50pit-0.02piy)]`
putting `x=25` and `t=(1)/(200)s`.
`v_(p)=-(2000pi cm//s)sin[50pi((1)/(200))-0.02pi(25)]`
`=10pisqrt(2) m//s`