# Room acoustics

Room acoustics describes how sound behaves in an enclosed space. Sound of different frequencies behaves differently in a room. Reflections between walls, floor and ceiling create room modes at specific frequencies and locations. Reflections also produce reverberation.

## Frequency zones

The way that sound behaves in a room can be broken up into roughly four different frequency zones:

• The first zone is below the frequency that has a wavelength of twice the longest length of the room. In this zone, sound behaves very much like changes in static air pressure.
• Above that zone, until wavelengths are comparable to the dimensions of the room,[a] room resonances dominate. This transition frequency is popularly known as the Schroeder frequency, or the cross-over frequency and it differentiates the low frequencies which creates standing waves within small rooms from the mid and high frequencies.[3]
• The third region which extends approximately 2 octaves is a transition to the fourth zone.
• In the fourth zone, sounds behave like rays of light bouncing around the room.

## Natural modes

The sound wave has reflections at the walls, floor and ceiling of the room. The incident wave then has interference with the reflected one. This action creates standing waves that generate nodes and high-pressure zones.[4]

A modal density analysis method using concepts from psychoacoustics, the "Bonello criterion", analyzes the first 48 room modes and plots the number of modes in each one-third of an octave.[5] The curve increases monotonically (each one-third of an octave must have more modes than the preceding one).[6] Other systems to determine correct room ratios have more recently been developed.[7]

## Reverberation of the room

After determining the best dimensions of the room, using the modal density criteria, the next step is to find the correct reverberation time. The most appropriate reverberation time depends on the use of the room. Times about 1.5 to 2 seconds are needed for opera theaters and concert halls. For broadcasting and recording studios and conference rooms, values under one second are frequently used. The recommended reverberation time is always a function of the volume of the room. Several authors give their recommendations [8] A good approximation for broadcasting studios and conference rooms is:

TR[1 kHz] = [0.4 log (V+62)] – 0.38 seconds,

with V=volume of the room in m3.[9] Ideally, the RT60 should have about the same value at all frequencies from 30 to 12,000 Hz.

To get the desired RT60, several acoustics materials can be used as described in several books.[10][11] A valuable simplification of the task was proposed by Oscar Bonello in 1979.[12] It consists of using standard acoustic panels of 1 m2 hung from the walls of the room (only if the panels are parallel). These panels use a combination of three Helmholtz resonators and a wooden resonant panel. This system gives a large acoustic absorption at low frequencies (under 500 Hz) and reduces at high frequencies to compensate for the typical absorption by people, lateral surfaces, ceilings, etc.

## Notes

1. ^ The frequency is approximately ${\displaystyle 2000{\sqrt {{\textit {RT60}}/{\textit {V}}}}}$  Hz when room volume V is measured in cubic metres and reverberation time TR60 is measured in seconds; this formula incorporates the approximate speed of sound in air.[1][2]

## References

1. ^ Schroeder, Manfred (1996). "The 'Schroeder frequency' revisited". Journal of the Acoustical Society of America. 99 (5): 3240–3241.
2. ^ "Sound System Engineering" 4th edition, Don Davis, Eugene Patronis, Pat Brown, June 2013, page 215
3. ^ "Handbook of Noise and Vibration Control", Malcolm J. Crocker, 2007, page 54
4. ^ “Acoustics”, Leo Beranek, chapter 10, McGraw Hill Books, 1954
5. ^ Oscar Bonello, "A New Criterion for the Distribution of Normal Room Modes", Journal of the Audio Engineering Society (USA) Vol. 29, Nr. 9 – September/1981.
6. ^ Handbook for Sound Engineers Glen Ballou, Howards Sams Editors, page 56.
7. ^ Cox, TJ, D'Antonio, P and Avis, MR 2004, "Room sizing and optimization at low frequencies", Journal of the Audio Engineering Society, 52 (6), pp. 640–651.
8. ^ “Acoustics”, Leo Beranek, chapter 13, McGraw Hill Books, 1954
9. ^ "Clases de Acústica", Oscar Bonello, Edited CEI, Facultad de Ingeniería UBA
10. ^ Rettinger, Michael (1977). Acoustic Design and Noise Control. New York: Chemical Publishing.
11. ^ Knudsen, Vern Oliver; Cyril M. Harris. Acoustical designing in Architecture. New York: John Wiley and Sons.
12. ^ "A new computer aided method for the complete acoustical design of broadcasting and recording studios", Oscar Bonello, 1979 IEEE International Conference on Acoustics, Speech and Signal Processing, Washington