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. \(\omega = (\vec \omega \cdot {\vec e}_x)\), i.e. the angular frequency is a positive quantity if the wave travels in the positive direction of the \(x\)-axis. Here \({\vec e}_x\) 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:

\(\varphi\)

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:

\[\varphi = k x - \omega t\]