Question

A wave is modeled by the wave function.

y(x,t)= (0.30m)sin[2pi/4.50m(x-18.00m/st)].

What are the amplitude,wavelength,wave speed, period, and frequency of the wave?

Answer 1

The wave function is given by

$$y(x,t)= (0.30\:m)\sin\left[\frac{2\pi}{4.50\:\rm m}(x-18.00\frac{m}{s}t)\right]$$

The general form of a wave function is as follows

$$y(x,t)= A\sin\left[\frac{2\pi}{\lambda}(x-vt)\right]$$

Hence,

(a) the amplitude of a wave

$$A=0.30\:\rm m$$

(b) the wavelength of a wave

$$\lambda =4.50\:\rm m$$

(c) the speed of a wave

$$v=18.0\:\rm m/s$$

(d) the period of a wave

$$T=\lambda/v=\rm 4.50\: m/18.0\: m/s=0.25\: s$$

(e) the frequency of a wave

$$f=1/T=\rm 1/0.25\: s=4 \: Hz$$