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:

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:

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