Speed of wave depends mainly on four factors. These factors are wavelength, frequency, medium and temperature.
We know from laws of refraction, when a wave travels from rarer to denser medium, the speed of wave slows down. And when it travels from denser to rarer, it speeds up.
The relation of speed of wave with its wavelength and frequency is given by the following:
[tex]v = \lambda \times f[/tex]
The speed of a wave in a particular medium remains constant. A higher frequency wave has shorter wavelength.
The speed of a wave also varies with temperature in a given medium. temperature affects the density of the medium and vibrations of the medium particles. Higher the temperature, higher is the speed of wave.