The equation of a plane progressive wave travelling along positive direction of `x-`axis is `y=r sin [(2pit)/(T)-(2pix)/(lambda)]` where `y=` displacement of particle at `(x,t),r=` amplitude of vibratio of particle, `T=` time period of wave motion, `lambda=` wavelength of wave ,` x=` starting distance of wave from the origin. Velocity of wave,
`upsilon=vlambda=(lambda)/(T)=` constant.
Acceleration of wave, `a=0`.
Velocity of particle at time `t=(dy)/(dt)`
Acceleration of particle at time `t=(d^(2)y)/(dt^(2))`
Amplitude of particle velocity is

Options

A. `1.25xx10^(-4)m//s`
B. `1.25xx10^(-4)cm//s`
C. `0.125cm//s`
D. `0.125m//s`

Answer

D

Explanation

Amplitude of particle velocity
`rxx(2pi)/(T)=0.25xx10^(-3)xx(2pi)/(pi//250)`
`=0.25xx10^(-3)xx500`
`=0.125m//s`