Wavelength of a sine wave, λ, can be measured between any two points with the same phase, such as between crests, or troughs, or corresponding zero crossings as shown.As a wave travels by, the value at a given point oscillates sinusoidally.
One of the simplest formalisms of a plane wave involves defining it along the direction of the x-axis.
In the above equation…
is the magnitude or disturbance of the wave at a given point in space and time. For example, in the case of a sound wave, could be chosen to represent the excess air pressure.
is the amplitude of the wave (the peak magnitude of the oscillation).
is the wave’s wave number or more specifically the angular wave number and equals , where is the wavelength of the wave. has the units of radians per unit distance.
is a given point along the x-axis. and are not part of the equation because the wave's magnitude is the same at every point on any given y-z plane. This equation defines what that magnitude is.
is the wave’s angular frequency which equals , where is the period of the wave. has the units of radians per unit time.
is a given point in time
is the phase shift of the wave and has the units of radians. Note that a positive phase shift, at a given moment of time, shifts the wave in the negative x-axis direction. A phase shift of radians shifts it exactly one wavelength.
Other formalisms which directly use the wave’s wavelength , period , frequency and velocity are below.
With regards to the above set of equations it is noteworthy that and
![{\displaystyle A=A_{o}sin[2\pi (x/\lambda -t/T)+\varphi ]\,\!}](https://wikimedia.org/api/rest_v1/media/math/render/svg/d7c4f25ee6b55f173dcd1985ab910d0fed7f9109)
![{\displaystyle A=A_{o}sin[2\pi (x/\lambda -ft)+\varphi ]\,\!}](https://wikimedia.org/api/rest_v1/media/math/render/svg/d4b6281b9ec54764f115d8193d8c53cf8b11fac6)
![{\displaystyle A=A_{o}sin[(2\pi /\lambda )(x-ct)+\varphi ]\,\!}](https://wikimedia.org/api/rest_v1/media/math/render/svg/1b057a08dc1f2a60a301e52e326aa9a32f86e8bf)
