A progressive wave is described by the equation `y = 0.1 sin (100 pit - 8pi x)`, where x and y are in metre and t is in second. What is the velocity of an oscillating particle (P) of the medium, which is at a distance of `(29)/(24)` m from the source point at time `t = 0.1 s` ?

Options

A. `5pi m//s`
B. `3pi m//s`
C. `4pi m//s`
D. `2pim//s`

Answer

A

Explanation

`y - 0.1 sin (100 pi t - 8pi x)`
`:. V_(P) = (dy)/(dt) = 0.1 xx 100pi xx cos (100 pi t - 8pi x)`
(for `x = (29)/(24) and t = 0.1s`)
`V_(P) = 10 pi cos [100pi xx 0.1 - 8pi xx (29)/(24)]`
`= 10 pi cos [10 pi - (29pi)/(3)]`
`= 10pi "cos" (pi)/(3) = 5pi m//s`