In a progressive wave `y = 5 sin (100 pi t - 0.4 pi x)` when and x are in metre, t is in second. What is the particle velocity amplitude?

Options

A. `200pi m//s`
B. `300 pi m//s`
C. `400 pi m//s`
D. `500 pi m//s`

Answer

D

Explanation

`y = 5 sin (100 pi t - 0.4 pi x)`
`:.` The particle velocity `= (dy)/(dt)`
`= 5 (100pi) cos (100 pi t - 0.4 pi x)`
The particle velocity `((dy)/(dt))` is maximum, when `[cos 100 pi t - 0.4 pi x] = 1`
`:.` Max. particle velocity `= 5 xx 100 pi xx 1 = 500 pi m//s`