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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.
Spatial position Position of a point in space, not necessarily a point on the wave profile or any line of propagation d, r: m [L] Wave profile displacement Along propagation direction, distance travelled (path length) by one wave from the source point r 0 to any point in space d (for longitudinal or transverse waves) L, d, r
A standing wave, also known as a stationary wave, is a wave whose envelope remains in a constant position. This phenomenon arises as a result of interference between two waves traveling in opposite directions. The sum of two counter-propagating waves (of equal amplitude and frequency) creates a standing wave. Standing waves commonly arise when ...
In mechanics and physics, simple harmonic motion (sometimes abbreviated as SHM) is a special type of periodic motion an object experiences by means of a restoring force whose magnitude is directly proportional to the distance of the object from an equilibrium position and acts towards the equilibrium position.
Since the only wavefunction that can have lowest position-momentum uncertainty, , is a gaussian wavefunction, and since the coherent state wavefunction has minimum position-momentum uncertainty, we note that the general gaussian wavefunction in quantum mechanics has the form: (′) = ^ (′ ^ ) (′ ^ ).
The position at a given time t also depends on the phase φ, which determines the starting point on the sine wave. The period and frequency are determined by the size of the mass m and the force constant k , while the amplitude and phase are determined by the starting position and velocity .
In most cases this is a longitudinal wave of pressure (such as sound), but it can also be a transverse wave, such as the vibration of a taut string. In the case of a sound wave travelling through air, the particle displacement is evident in the oscillations of air molecules with, and against, the direction in which the sound wave is travelling. [2]
The interference involves different types of mathematical functions: A classical wave is a real function representing the displacement from an equilibrium position; an optical or quantum wavefunction is a complex function. A classical wave at any point can be positive or negative; the quantum probability function is non-negative.