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The wavelength of a sine wave, λ, can be measured between any two points with the same phase, such as between crests (on top), or troughs (on bottom), or corresponding zero crossings as shown. In physics and mathematics, wavelength or spatial period of a wave or periodic function is the distance over which the wave's shape repeats.
The phase velocity is given in terms of the wavelength λ (lambda) and period T as =. A wave with the group and phase velocities going in different directions Group velocity is a property of waves that have a defined envelope, measuring propagation through space (that is, phase velocity) of the overall shape of the waves' amplitudes ...
When two signals with these waveforms, same period, and opposite phases are added together, the sum + is either identically zero, or is a sinusoidal signal with the same period and phase, whose amplitude is the difference of the original amplitudes. The phase shift of the co-sine function relative to the sine function is +90°.
where ν is the frequency of the wave, λ is the wavelength, ω = 2πν is the angular frequency of the wave, and v p is the phase velocity of the wave. The dependence of the wavenumber on the frequency (or more commonly the frequency on the wavenumber) is known as a dispersion relation.
The phase velocity is given in terms of the wavelength λ (lambda) and time period T as =. Equivalently, in terms of the wave's angular frequency ω, which specifies angular change per unit of time, and wavenumber (or angular wave number) k, which represent the angular change per unit of space,
with T the wave period (the reciprocal of the frequency f, T=1/f). So in deep water the phase speed increases with the wavelength, and with the period. Since the phase speed satisfies c p = λ/T = λf, wavelength and period (or frequency) are related. For instance in deep water:
Quantity (common name/s) (Common) symbol/s SI units Dimension Number of wave cycles N: dimensionless dimensionless (Oscillatory) displacement Symbol of any quantity which varies periodically, such as h, x, y (mechanical waves), x, s, η (longitudinal waves) I, V, E, B, H, D (electromagnetism), u, U (luminal waves), ψ, Ψ, Φ (quantum mechanics).
The relationship between the wavelength, period and velocity of any wave is: = / where C is speed (celerity), L is the wavelength, and T is the period (in seconds). Thus the speed of the wave derives from the functional dependence () of the wavelength on the period (the dispersion relation).