Phase of traveling wave

The phase of a wave or other periodic function of some real variable $t$ is an angle-like quantity representing the fraction of the cycle covered up to $t$. As the variable $t$ completes a full period, the phase increases by ${360}^{\circ }$ or $2\pi$.

If a function $h(x,t)$ describes a traveling wave, then position $x$ and time $t$ can only appear in the form of the wave phase described below.

Notes:

1. $\omega =(\overrightarrow{\omega }\cdot {\overrightarrow{e}}_x)$, i.e. the angular frequency is a positive quantity if the wave travels in the positive direction of the $x$-axis. Here ${\overrightarrow{e}}_x$ is the unit vector pointing in the positive direction of the $x$-axis.

Conditions:

1. This law applies to a 1-dimensional traveling wave.

2. The constant phase shift is not taken into account.

Links:

1. Wikipedia, similar formula.

wave_phase

phase of the wave.

Symbol:

phi

Latex:

$\phi$

Dimension:

angle

angular_wavenumber

angular_wavenumber of the wave.

Symbol:

k

Latex:

$k$

Dimension:

angle/length

position

position, or spatial coordinate.

Symbol:

x

Latex:

$x$

Dimension:

length

angular_frequency

angular_frequency of the wave.

Symbol:

w

Latex:

$\omega$

Dimension:

angle/time

time

time.

Symbol:

t

Latex:

$t$

Dimension:

time

law

phi = k * x - w * t

Latex:

$$\phi =kx-\omega t$$