The equation of a travelling plane sound wave has the form `y=60 cos (1800t-5.3x)`, where y is in micrometres, t in seconds and x in metres. Find
(a). The ratio of the displacement amplitude with which the particle of the medium oscillate to the wavelength,
(b).the velocity oscillation ammplitude of particles of the medium and its ratio to the wave propagation velocity , (c). the particle acceleration amplitude.

Explanation

Comparing with the standard form `y=a cos (omegat-ks)`.
`omega=1800` or `f=(1800//2pi)`
and `k=5.3` or `lambda=2pi//5.3 m`
`a=60xx10^(-6) m`
(a). `v=(dy)/(dt)=-aomega sin(omegat-kx)` (b). `V=(dy)/(dt)=-aomega sin(omegat-kx)`
`:. V_(max)=aomega`
`V_(max)=60xx10^(-6)xx1800=0.108 m//s`
`c=f lambda=(1800)/(2pi)xx(2pi)/(5.3)=339.6 m//s`
`:.(v_(max))/(c)=(0.108)/(339.6)=3.18xx10^(-4)`