A sinusoidal wave travelling in the positive `x` direction has an amplitude of `15 cm`, wavelength `40 cm` and freqency `8 Hz`. The vertical displacement of the medium at `t = 0` and `x = 0` os also `15 cm`, as shown.

(a) Find the angular wave number, period, angualr frequency and speed of the wave.
(b) Datermine the phase constant `phi`, and write a general expression for the two wave function.

Explanation

(a) `k = (2pi)/(lambda) = (2pirad)/(40 cm) = (pi)/(20) rad//cm`
`t = (1)/(f) = (1)/(8) s , omega = 2pif = 16 s^(-1)`
`v = flambda = 320 cm//s`
(b) It is given that `A = 15 cm`
and also `y = 15 cm` at `x = 0` and `t = 0`
then using `y = A sin (omegat - kx + phi)`
`15 = 15 sin phi rArr sin phi = 1`
or `phi = (pi)/(2) rad`.
Therefore, the wave funcation is
`y = A sin (omegat - kx + (pi)/(2))'`
`= (15 cm) sin [(16pis^(-1))t - ((pi)/(20)(rad)/(cm)) x + (pi)/(2)]`