Question

A sinusoidal wave travelling in the positive x-direction has a wavelength of 0.4 m, an amplitude of 20 cm, and a period of 4 seconds. The transverse position of an element of the medium at x = 0 and t = 0 is y = 10 cm, and the element is moving downward. The expression of the wave function describing this wave is:

Answer 1

In general, the sinusoidal wave is described by

$$y(x,t)=A\sin(\omega t-kx+\phi_0)$$

In our case,

$$A=0.2{\:\rm m}\\ \omega=2\pi/T=2\pi/4=0.5\pi\\ k=2\pi/\lambda=2\pi/0.4=5\pi\\ \phi_0=\pi/2$$

Finally

$$y(x,t)=0.2\sin(0.5\pi t-5\pi x+\pi/2)\\ =0.2\cos(0.5\pi t-5\pi x)$$