# Transition Frequency

In a hybrid calculation, you need to specify the frequency where the transition between the wave-based solver and the geometrical solver solver occurs. A large transition frequency means that the former will run over a larger frequency range, and reciprocally. We do suggest an appropriate transition frequency for your model based on consensual guidelines within the acoustics community (as discussed below). However, this choice is always to some extent a compromise between accuracy and calculation speed.

When at least two waves superimpose, which is likely to happen in a room due to the many reflections off the boundaries, positive and negative pressures are added at every point in space and time. This results in a so-called standing wave or interference pattern, which happens at the natural frequencies (or eigen-frequencies) of a room, resulting in a higher sound pressure level at those frequencies. These are also called room modes, and are mainly determined by the dimensions of the room. The room modes play a paramount role at low frequencies, but they start to overlap very quickly as the frequency increases (the number of oblique room modes is a cubic function of frequency). Then the exact information from individual modes is getting less crucial in analyzing the sound field.

The **Schroeder frequency** is a well-established metrics which represents the frequency at which the modal overlap is threefold [1], i.e., at least three modes fall within the half-power bandwidth of one mode. It is defined as

where $T$ is the reverberation time [s] and $V$ is the volume of the room [m³]. A consensus in the room acoustics community is to set the transition frequency in the simulations to one to four times the Schroeder frequency. Treble by default suggests a transition frequency equal to four times the Schroeder frequency for the considered room volume, using an initial guess for the reverberation time of one second. Note that the Schroeder frequency needs the prior knowledge of $T$ (which is unknown and one of the main purposes of the simulation), so this suggestion is an approximation.

## References

[1] M. R. Schroeder. The ‘‘Schroeder frequency’’ revisited. J. Acoust. Soc. Am., 99:3240, 1996.