Speed of a Travelling Wave

A handy formula for wave speed is easy to get! In one complete cycle the wave travels a distance x = λ and takes a time t = T to do it. Thus the wave speed must be

Simple algebra also gives

Example What is the amplitude, wavelength, frequency and speed of the wave described by

with all quantities in SI units (i.e. 5 m, 3 m^-1 and 2 sec^-1).

Solution The general wave is

Thus the amplitude is

the wave number is

and angular frequency is

Now  giving

and  giving

and the speed is