The speed of a wave is a property of the medium. If the medium does not change as a wave travels, the wave speed is constant.

In one period the wave travels one wavelength. Speed is distance over time, so:

v

=

λ T

The frequency f = 1/T, so v = fλ

This makes it look like speed is determined by frequency and wavelength, but that is not the case. The speed is set by the medium itself.

A good example is a wave on a stretched string. For a string with a tension T and a mass per unit length μ, the wave speed is given by:

v

=

(

T μ

)

½

This is generally true - the wave speed is typically proportional to the square root of the elastic property divided by the inertial property.