Discuss the 3d wave equation in spherical coordinates, and then reduce it to a 2d wave equation by taking the case that the radius of the ball is fixed, such that all the radial derivatives vanish.

Respuesta :

The wave equation is a second-order linear partial differential equation that describes waves as mechanical waves (such as sound, light, and water waves) or as electromagnetic waves (such as seismic waves).

It comes from disciplines like fluid dynamics, acoustics, and electromagnetics. The second-order wave equation is sometimes known as a "two-way wave equation" because it explains a standing wave field, which is the superposition of an incoming wave and an outgoing wave (in contrast, a first-order one). Due to the first-order derivatives, the -way wave equation, which represents a single wave with a specific wave propagation direction, is relatively simple to calculate.

The wave equation's representation of a pulse moving through a string with fixed ends.

Emanating from a single point source, spherical waves.

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