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The wave equation is a second-order linear partial differential equation for the description of waves or standing wave fields such as mechanical waves (e.g. water waves, sound waves and seismic waves) or electromagnetic waves (including light waves). It arises in fields like acoustics, electromagnetism, and fluid dynamics.
Boussinesq approximation (water waves) – Approximation valid for weakly non-linear and fairly long waves; Mild-slope equation – Physics phenomenon and formula; Shallow water equations – Set of partial differential equations that describe the flow below a pressure surface in a fluid; Stokes drift – Average velocity of a fluid parcel in a ...
Eventually, a steady state is reached where the string has identical right- and left-traveling waves as in the infinite-length case and the power dissipated by damping in the string equals the power supplied by the driving force so the waves have constant amplitude. Equation still describes the standing wave pattern that can form on this string ...
Intuitively the wave envelope is the "global profile" of the wave, which "contains" changing "local profiles inside the global profile". Each propagates at generally different speeds determined by the important function called the dispersion relation.
The horizontal momentum equations of the mean flow requires this additional wave-induced flux to be balanced: this causes a decrease in the mean water level before the waves break, called a "setdown". After the waves break, the wave energy flux is no longer constant, but decreasing due to energy dissipation. The radiation stress therefore ...
An equation used to model this relationship is called an equation of state. In most cases this model will comprise some empirical parameters that are usually adjusted to measurement data. Equations of state can also describe solids, including the transition of solids from one crystalline state to another.
The Dirac equation is a relativistic wave equation detailing electromagnetic interactions. Dirac waves accounted for the fine details of the hydrogen spectrum in a completely rigorous way. The wave equation also implied the existence of a new form of matter, antimatter, previously unsuspected and unobserved and which was experimentally confirmed.
The case = is called the ground state, its energy is called the zero-point energy, and the wave function is a Gaussian. [23] The harmonic oscillator, like the particle in a box, illustrates the generic feature of the Schrödinger equation that the energies of bound eigenstates are discretized. [11]: 352