# Room eigenmodes

Room eigenmode (1 2 1): Representation of the square value of the sound pressure at the walls of the room. Dark areas correspond to a high sound pressure or high loudness.

Sound propagation at frequencies below the limiting frequency of a room is determined by the room’s eigenmodes. These are three-dimensional standing waves that can be excited at the characteristic eigenfrequencies of the room. Each eigenmode is associated with a different sound pressure distribution. A sound pressure receiver such as the human ear or a microphone moving around in a room that has been excited at such an eigenfrequency will register strongly fluctuating sound intensities.

The frequencies at which these room resonances occur as well as their sound pressure distribution depend, among other things, on the geometry and size of the room. For rectangular rooms the eigenfrequencies can be calculated by means of a simple formula. For rooms with other shapes, however, time-consuming numerical methods must be used.

The Room Eigenmodes Calculator determines the first 20 eigenfrequencies for rectangular rooms and presents them in ascending order. To distinguish between the different eigenmodes a combination of three natural numbers is used (*nx ny nz*). You would, for example, speak of room eigenmode (1 2 1).

In order to achieve good acoustics it is desirable that the eigenfrequencies are uniformly distributed, and that no accumulations occur near to a particular frequency. If the room was a cube with edges of 2 m length many eigenfrequencies would coincide. The room eigenmodes (2 0 0), (0 2 0) and (0 0 2), for example, would all be excited at a frequency of 171.5 Hz. This coincidence of eigenfrequencies occurs whenever one dimension of a room is an integer multiple of another such as, e.g., in a room that is twice as wide as it is high. Favorable spatial proportions, on the other hand, would be 1/1.4/1.9 or 1/1.6/2.1.