Question

A plane progressive wave is give by `x=(40 cm) cos (50pit-0.02piy)` where y is in centimetres and t in seconds. What will be the particle velocity at `y=25 cm "in time" `t=1//200 s?

Answer 1

Given that `x=40 cos (50pi t-0.02pi y)`
Therefore, particle velocity can be given as
`v_(p)pi(dx)/(dt)pi(40xx50pi){-sin(50pit-0.02pi y)}`
puttting `x=25` and `t=(1)/(200)s`,
`v_(p)-(2000pi cm//s)sin[50pi((1)/(200))-0.02pi(25)]`
`10pisqrt(2)m//s`