A simple harmonic travelling wave is represented by `y=50sinpi(20t-0.08x)` is SI units. Find its amplitude, time period and wavelength. Also, calculate maximum particle velocity.

Explanation

The given equation is
`y=50sinpi(20t-0.08x)`
`=50sin(20pit-(8pi)/(100)x)`
Compare it with standard equation of wave motion
`y=rsin((20pit)/(T)-(2pix)/(lambda))`
`r=50m, (2pi)/(T)=20pi, T=(2)/(20)=0.1s`
`(2pi)/(lambda)=(8pi)/(100), lambda=25m`
Maximum particle velocity
`upsilon_(max.)=romega =r(2pi)/(T)`
`=50xx20pi`
`=1000xx3.1416=3141.6m//s`