Displacement in standing wave¶

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

Notes:

In this law we assume the standing wave to be composed of two identical traveling sinusoidal waves of the form \(u_\text{max} \sin(k x \pm \omega t)\)
A standing wave is no longer a traveling one because it doesn’t move in a single direction.

Links:

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¶

Symbol:: t
Latex:: \(t\)
Dimension:: time

law¶

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

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