Position of antinodes in standing wave

In a standing wave, the locations of maximum amplitude are called antinodes. These locations are not arbitrary, however, and are integer multiples of half the wavelength shifted by a quarter of the wavelength.

Notes:

  1. Amplitude refers to the absolute value of displacement from rest, therefore positions of maximum amplitude are such positions where the displacement is maximum or minimum.

Links:

  1. Wikipedia.

antinode_position

position of \(m\)-th antinode.

Symbol:

x

Latex:

\(x\)

Dimension:

length

integer_factor

An integer. See whole_number.

Symbol:

N

Latex:

\(N\)

Dimension:

dimensionless

wavelength

wavelength of the standing wave.

Symbol:

lambda

Latex:

\(\lambda\)

Dimension:

length

law

x = (N + 1 / 2) * lambda / 2

Latex:
\[x = \frac{\left(N + \frac{1}{2}\right) \lambda}{2}\]