Acoustics, Noise Control, Audio Systems and Lighting

**Room Acoustics**

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):

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 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.

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.

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 ft
V ft³

Hz
Hz
Hz

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 and in the "examples" page:

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.