wave equation

C 2 \ Nabla 2u \ Partial 2 University

Here c is usually a fixed constant, that is, the propagation speed of waves (sound waves in air are about 330m/s, see the speed of sound). For the vibration of a string, this can vary greatly: on slinky, it can be as slow as 1 m/s, but if c changes as a function of wavelength, it should be replaced by phase velocity:

v_\mathrm = \frac{\omega}。

Please note that waves may be superimposed on other movements (for example, the propagation of sound waves in moving media such as airflow). In this case, the scalar u will contain a Mach factor (positive for waves moving along the coastal current and negative for reflected waves).

U = u(x, t), which is a measure of the amplitude and wave intensity at a specific position x and a specific time t, is the local air pressure for sound waves in the air, and the displacement from a static position for vibrating strings. \ nabla 2 is a Laplacian operator relative to the position variable x, note that u can be a scalar or a vector.

Wave equation: