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 $u_{\text{max}}\sin (kx\pm \omega t)$

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:

$$u=2u_{\text{max}}\sin (kx)\cos (\omega t)$$