Physical and Geometrical (Ray) Acoustics
Sound behavior in a room depends significantly on the ratio of the frequency (or the wavelength) of the sound to the size of the room. Therefore, the audible spectrum can be divided into four regions illustrated in the following drawing (for a rectangular room and dimensions are in ft):

L (10 to 1000) ft    V (1000 to 100000) ft³   

Calculate frequencies f1, f2 and f3   Hz   Hz   Hz  

Modes
Modes are the resonant frequencies on which the waves interface and form maximums and minimums of sound pressure at different points in the room. The distribution of resonant frequencies over the audible spectrum is not uniform.

The spectrum of resonant frequencies is discrete for low frequencies and continuous at the higher frequencies as shown in the following illustration. The larger the room, the lower frequency range of the continuous spectrum. The reverberant decay in locations of the maximum sound pressure will be longer, therefore, the frequency distortion occurs for sounds with the discrete resonant spectrum.

The calculation of modes in a rectangular enclosure is simple. The modes become complex and sometimes unpredictable in rooms of complex shapes. There are 3 types of modes: axial (two parallel surfaces contribute to the mode), tangential (4 surfaces) and the oblique mode (6 surfaces).

The lowest frequency of all modes is for the axial mode, and it can be calculated from f=C/2L, where C is the speed of the sound and L is the room length.

It is important to note that the modes of the enclosure are weak (in pressure amplitude) when the walls are sound absorbing. To splay the walls (in music practice rooms for example) makes modes unpredictable and less organized which, sometimes, can weaken the well-defined structure of the maximum and minimum values of the sound pressure.

Sound Diffusion and Diffusers
Sound in an enclosure can be described as a diffused, if the intensity of the sound energy is equal in every location of the room, or the sound energy flows equally in every direction.

Many different factors can enhance the diffused sound. These factors include geometrical irregularities, absence of focusing surfaces, the distribution of absorptive and reflective elements randomly scattered through the space, and the existence of diffusing objects (furniture) or panels (diffusers).

Diffusing panels scatter the sound in all, or in certain directions depending on their type and geometrical dimension. A new type of diffusers is the Schroeder diffuser (Quadratic-residue diffusers). Its diffusion characteristics do not depend solely on its geometrical dimensions, but also on an array of wells with depths determined by a listed quadratic residue sequence.

Reverberation Time (RT)
Reverberation time is the time required for the sound level in the room to decay 60 dB, or in other words, it is the time needed for a loud sound to be inaudible after turning off the sound source. This concept is shown in the following drawing:

The calculation of reverberation time using Sabine or Eyring equations assumes that the sound in the room be diffused. In practice, RT equations are good enough to describe the sound build up and attenuation in the room.

In the case where the sound in the room is not diffused enough, such as rooms with good absorption surfaces in some areas, or with an unusual shape (long and narrow, very low ceiling, or many different focusing surfaces), the RT calculation is not accurate. There is the Fitzroy equation to correct the RT calculation for rooms with good absorptive surfaces on one (or more) axis of the room.

The optimum reverberation time for different rooms depends on the volume of the space, the type of the room, and the frequency of the sound. In general terms, the optimum RT for rooms with speech programs is less than the optimum RT for rooms with music performance.

Reflector
A smooth-surface panel is considered a sound reflector if it meets the conditions illustrated in the following figure:

Acoustical Simulation
Acoustical simulation is a technique that assists the acoustical consultants in the evaluation of room acoustics and the performance of the sound systems. This acoustical program can simulate the sound as it would be heard after the project is built. This is called auralization.

The physical data of the room is entered into the program. AutoCAD file can be used to transfer the data to the program. The data entry includes surface materials, background noise, and the seating layout.

Some of the acoustical factors that can be studied in these acoustical programs include reverberation time, intelligibility, echo, and sound levels over the seating areas.