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The amplitude of a periodic variable is a measure of its change in a single period (such as time or spatial period) A true plane wave cannot physically exist. Traveling sinusoidal waves are often represented mathematically in terms of their velocity v (in the x direction), frequency f and wavelength λ as

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Where y is the value of the wave at any position x and time t, and a is the amplitude of the wave And the scalar is its phase shift They are also commonly expressed in terms of wavenumber k (2π times the reciprocal of wavelength) and angular frequency ω (2π times the frequency.

Wavenumber, as used in spectroscopy and most chemistry fields, [5] is defined as the number of wavelengths per unit distance

Ν ~ = 1 λ , {\displaystyle {\tilde {\nu }}\;=\ {\frac {1} {\lambda }},} where λ is the wavelength It is sometimes called the spectroscopic wavenumber [1] it equals the spatial frequency

[6] in theoretical physics, an angular wave number, defined as the number. Particle displacement or displacement amplitude is a measurement of distance of the movement of a sound particle from its equilibrium position in a medium as it transmits a sound wave [1] the si unit of particle displacement is the metre (m) 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

For one spinless particle in one dimension, if the wave function is interpreted as a probability amplitude

The square modulus of the wave function, the positive real number is interpreted as the probability density for a measurement of the particle's position at a given time t. In physics, a wave vector (or wavevector) is a vector used in describing a wave, with a typical unit being cycle per metre It has a magnitude and direction Its magnitude is the wavenumber of the wave (inversely proportional to the wavelength), and its direction is perpendicular to the wavefront.

Depending on context, wave height may be defined in different ways [1] h = 2 a [1] h = max { η ( x − c p t ) } − min { η ( x − c p t. The term is also used, even more specifically, to mean a monochromatic or sinusoidal plane wave

A travelling plane wave whose profile is a sinusoidal function

That is, the parameter , which may be a scalar or a vector, is called the amplitude of the wave The scalar coefficient is its spatial frequency