Standing Waves


Standing waves are stationary waves


A standing wave is the vibration state of a stable system. An example of this is the vibrating string of a musical instrument, or the column of air in an organ pipe.
These waves have a “wave-like” look, but nothing is moving.
The string is clamped between two fixed ends with length L which is called a node also known as a zero crossing. The location directly between two nodes is called an antinode.

Shown below are the natural vibrations of an idealized string, which is assumed to be perfectly flexible. The stiffness is assumed to be zero. The frequencies of the vibrations form harmonics, also called partials.

c= speed of sound
L = length of the string


The fundamental wave is known as the first harmonic.

1st Harmonic

2nd Harmonic

3nd Harmonic

4th Harmonic


Note:
The distance between two nodes (knots) or two maxima ( antinodes ) is λ/2.
The distance between a node (maximum) and an ntinode (minimum) is λ/4.


The room resonances formed between the boundary surfaces of a room, are called "standing waves" or room modes, or modes. They arise if a multiple of half the wavelength (λ/2) fits between the boundary surfaces of an area. Therefore, one need not necessarily parallel walls.

In practice only low frequencies as sound pressure below 300 Hz are considered as room modes. Higher modal frequencies become less important, because their disturbing effect is masked by other acoustic effects. On the walls there are formed by the modes always sound pressure maxima - that are sound pressure antinodes.

Take a look at my Room Modes Calculator