A wave travelling along a strong is described by
`y(x,t)=0.005 sin (80.0x-3.0t)`
in which the numerical constants are in SI units `(0.005m, 80.0 rad m^(-1)` and `3.0 rad s^( -1))`. Calculate (a) the amplitude. (b) the wavelength (c) the period and frequency of the wave. Also , calculate the displacement y of the wave at a distance `x=30.0` cm and time t=20 s?

Explanation

On comparing this displacement equation with, `y(x,y)=asin(kx-omegat)`
(i) The amplitude of the wave is 0.005m=5mm.
The angular wave number k and angular frequency `omega` are `k=80.0m^(-1) and omega=3.0s^(-1)`
we then relate the wavelength `lamda` to k through `lamda=2pi//k=7.85cm`
(iii) Now we relate T to `omega` by the relation `T=2pi//Omega=2.09s` and frequency `v=1//T=0.48Hz`.