In mathematics, a wave is often conceptualized as a periodic oscillation and can be represented by various functions, most commonly the sine and cosine functions. These mathematical waves are essential tools to understand and represent real-world phenomena in a variety of fields.

A general representation of a wave can be given by:

Where:

- is the amplitude, signifying the maximum value of the wave.
- is the wave number, related to the wavelength as .
- is the angular frequency, connected to the frequency as .
- is the phase shift, which determines the horizontal shift of the wave.
- represents the position, and denotes time.