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mathematical equation for wave. Tt c22u which models the vibrations of a string in one dimension u uxt the vibrations of a thin membrane in two dimensions u uxyt or the pressure vibrations of an acoustic wave in air u uxyzt. This is in contrast with more familiar linear partial differential equations such as the heat equation the wave equation and the Schroedinger equation of quantum physics 1 2.
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Angular frequency o - is 2 p times the frequency in SI units of radians per second. 2 u t 2 c 2 2 u x 2. The derivation of the wave equation certainly varies depending on context.
It takes the form wtt c2 wxx.
The wave equation in particular is exceedingly important. A more general form of the wave equation is. A careful study of the standing wave patterns of a vibrating rope reveal a clear mathematical relationship between the wavelength of the wave that produces the pattern and the length of the rope in which the pattern is displayed. 1717 discovered the wave equation in one space dimension.
