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A simple harmonic wave train of amplitud...

A simple harmonic wave train of amplitude 1 cm and frequency 100 vibration is travelling along positive x-direction with a velocity of `15ms^(-1)`. Calculate displacement y , the particle velocity and particle acceleration at `x=180cm` from the origin at `t=5` s.

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He`r=1cm, v=100`hertz, `upsilon=15m//s, y=?, (dy)/(dt)=? , x=180cm, t=5s`
Now, `lambda=(upsilon)/(v)=(1500)/(100)=15cm, T=(1)/(v)=(1)/(100)=0.01sec. `
The equation of the wave is `y=rsin[(2pit)/(T)-(2pix)/(lambda)]=1sin[(2pixx5)/(0.01)-(2pixx180)/(150)]`
`y=sin(1000pi-24pi)=sin976pi=0`
As, `sin[(2pit)/(T)-(2pix)/(lambda)]=0, cos[(2pit)/(T)-(2pix)/(lambda)]=1`
`:. (dy)/(dt)=rxx(2pi)/(T)cos((2pit)/(T)-(2pix)/(lambda))=1xx(2pi)/(0.010)xx1=200picm//s`
`(d^(2)y)/(dt^(2))=-rxx((2pi)/(T))^(2)sin[(2pit)/(T)-(2pix)/(lambda)]=zero`
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