A sinusoidal wave travelling in the positive direction on a stretched string has amplitude 2.0 cm, wavelength 1.0 m and wave velocity 5.0 m/s. Ar x = 0 and t = 0, it is given that `y=0 and (deltay)/(deltat)lt 0`. Find the dr wave function y(x, t).

Explanation

We start with a general form for a rightward moving wave. `y(x,t) =A sin (kx - omegat + phi)`.
The amplitude given is A= 2.0 cm=0.02 m.
The wavelength is given as, `lambda`= 1.0m
`:.` Wave number `k =(2pi)/lambda = 2pi m^(-1)`
Angular frequency `omega =vk = 10pi` red /s
`:. y (x,t) =(0.02) sin[2pi(x - 5.0t) +phi]`
We are told that for x = 0, t = 0, Y= 0 and `(deltay)/(deltat) lt 0`
From these conditions, we may conclude that `phi = 2 n pi`
where n=0, 2, 4, 6, ....... Therefore,
`y(x,t) = (0.02m) sin[(2pi m^(-1) ) x - (10pi s^(-1))t ] m`