Displacement in standing wave

A standing, or stationary, wave is the result of the interference of two identical waves moving in opposite directions.

Notes:

1. In this law we assume the standing wave to be composed of two identical traveling sinusoidal waves of the form \(u_\text{max} \sin(k x \pm \omega t)\)

2. A standing wave is no longer a traveling one because it doesn’t move in a single direction.

Links:

1. Physics LibreTexts, similar to formula 14.7.3.

total_displacement

Displacement of the resulting wave.

Symbol:

u

Latex:

\(u\)

amplitude

Amplitude of the interfering waves.

Symbol:

u_max

Latex:

\(u_\text{max}\)

angular_wavenumber

angular_wavenumber of the interfering waves.

Symbol:

k

Latex:

\(k\)

Dimension:

angle/length

position

position, or spatial coordinate.

Symbol:

x

Latex:

\(x\)

Dimension:

length

angular_frequency

angular_frequency of the interfering waves.

Symbol:

w

Latex:

\(\omega\)

Dimension:

angle/time

time

time.

Symbol:

t

Latex:

\(t\)

Dimension:

time

law

u = 2 * u_max * sin(k * x) * cos(w * t)

Latex:

\[u = 2 u_\text{max} \sin(k x) \cos(\omega t)\]