Sine Wave - General Form

General Form

In general, the function may also have:

• a spatial dimension, x (aka position), with wavenumber k
• a non-zero center amplitude, D

which looks like this:

The wavenumber is related to the angular frequency by:.

where λ is the wavelength, f is the frequency, and c is the speed of propagation.

This equation gives a sine wave for a single dimension, thus the generalized equation given above gives the amplitude of the wave at a position x at time t along a single line. This could, for example, be considered the value of a wave along a wire.

In two or three spatial dimensions, the same equation describes a travelling plane wave if position x and wavenumber k are interpreted as vectors, and their product as a dot product. For more complex waves such as the height of a water wave in a pond after a stone has been dropped in, more complex equations are needed.