A sinusoidal wave trsvelling in the positive direction on a stretched string has amplitude `2.0 cm`, wavelength `1.0 m` and velocity `5.0 m//s`. At `x = 0` and ` t= 0` it is given that `y = 0` and `(dely)/(delt) lt 0`. Find the 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`