The equation of a travelling sound wave is `y = 6.0 sin (600 t - 1.8 x)` where y is measured in `10^-5m`, t in second and x in metre. (a) Find the ratio of the displacement amplitude of the particles to the wavelength of the wave. (b) Find the ratio of the velocity amplitude of the particles to the wave speed.

Explanation

Comparing the equation with the standard from of the wave equation
`y=a sin(omegat-kx), where omega =2pif and k = 2pi//lambda`
Given that (i)`omega=500pi or f=250 Hz`
and `(2pi)/(lambda)=(500p0i)/(30)` or `lambda=(3)/(25)m=0.12 m`
(ii). `:. C=flambda` or C=250xx(3)/(25)=30 m//s`
(iii). `v("particle velocity") = (dy)/(dt)=aomega cos(omegat-kx)`
`:. v_(max)=aomega=0.01xx500pi=15.7 m//s`
(iv). f(particle acceleration)
`=(dv)/(dt)=aomega^(2) sin(omegat-kx)`
`:. f_(max)=aomega^(2)=0.01xx(500pi)^(2) = 2.47xx10^(4) m//s^(2)`