1. Auditorium Acoustics 1. Sound propagation (Free field)
Free field: the sound source is small enough to be considered a point source, located outdoors away from reflecting surfaces
Pressure is proportional to 1/r, where r is the distance from the source
Pressure is halved as the distance doubles
There is a 6 dB drop in sound pressure level as the distance doubles
Free fields only exist indoors in anechoic rooms (echo-free)

2. 1a. Sound propagation (Indoors)
Indoors, sound travels only a short distance before encountering walls and other obstacles
These obstacles either reflect of absorb sound according to the acoustic properties of the room
The reflection patterns are determined by the curvature of the surface
Reflection Surfaces

3. 2. Direct, early and reverberant sound
Direct sound traveling in air (344 m/s) would reach a listener in an auditorium after a time of 20 to 200 ms depending on the distance from the source
Shortly after, the same sound would reach the listener from various reflecting surfaces
Early sound - any of the first group of reflections arriving within 50 to 80 ms
After the early sounds, reflections arrive thick and fast from all directions
These reflections are smaller and closer together, merging after a time into reverberant sound

4. Interesting: A simple acoustical analysis of a room can be done by examining the nature of the direct, early and reverberant sound produced in that room
2a. Direct sound
In auditoriums, some sounds are non-directional: sounds that radiate essentially with the same intensity in all directions
Others, such as upper range frequencies of brass instruments, are directional
For low frequencies, localization is done based on the slight time difference in the time of arrival
For high frequencies, localization occurs through the difference in sound level caused by the sound shadow

5. 2b. Early sound 2c. Reverberant Sound
Rapidly varying early sounds are heard as reinforced direct sound if they reach the listener within 50 ms
For slowly varying early sounds, the limit is 80 ms
Precedence effect
The ear continues to deduce the direction of the source from the arrival of the first sound if successive sounds:
arrive within 35 ms
have spectra and time envelopes similar to the first sound
are not too much louder than the first
2c. Reverberant Sound
Reverberation sound in low levels reinforces the direct sound
However, excessive reverberation sound causes a loss of clarity

6. 3. Characteristics of reverberant sound
If the source emits continuous sound, the reverberant sound builds until an equilibrium level is reached
When the sound source stop, the reverberant sound falls off at a constant rate until it is inaudible
The reverberant level is reached when the rate at which energy is supplied by the source is equal to the rate at which the sound is absorbed
If the sound source were impulsive, an equilibrium state is never achieved

7. 3. Characteristics of reverberant sound (continued)
If sound energy would uniformly distributed throughout the room, its decay, would follow an exponential curve
This would produce a straight line curve for the sound pressure decay
c) In auditoriums, decay curves tend to have two different reverberation times
This may indicate an insufficient distribution of sound and can lead to a feeling of “dryness” in a hall even though the final reverberation time is within acceptable limits
d) Spikes in the decay curves result from storage of sound energy in resonances
Reverberation time (RT or T60) is usually defined as the time it takes for the sound level to decrease by 60 dB or double the time it takes for a 30 dB decrease

8. 4. Calculation of the reverberation time
Sound energy in the room depends on
the power of the source
the volume of the room
The rate at which that energy is absorbed depends on:
the area and absorption coefficients of all the surfaces in the room
Reverberation time (RT):
Generally, large rooms have longer reverberation times than do small rooms!
K – constant
V – volume of the room
A – absorption (effective surface area)
For a room with solid walls, which absorb very little sound, and an open window of area A, the reverberation constant is:

9. 4a. Absorption (effective surface area)
We can model rooms similarly to modeling the window of area A
We can assume an absorption coefficient, a, which depends on the amount of sound power absorbed
So any material having surface area S can be said to have A = Sa
Total absorption of the room is found by adding up the contributions from each surface exposed to the reverberant sound
Sometimes absorption is expressed in sabins or metric sabins
One sabin is the absorption of one square foot of open window

10. Absorption coefficients

11. This calculation leads to an unrealistically long reverberation time
Furnishings in room will contribute a substantial fraction of the total absorption
People are also good absorbers of sound
Air Absorption:
m – coefficient that depends on frequency, temperature and humidity

12. Concert halls
A concert hall is considered “intimate” if the delay time between direct and first reflected sounds is less than 20 ms
Sometimes reflecting surfaces are suspended from the ceiling
A study has shown listeners prefer concert halls in which ceilings are sufficiently high so that the first lateral reflection reaches the listener before the first overhead reflection
Other studies have shown that if the total energy of the lateral reflections is greater than that of the overhead reflections, the hall has a “spatial responsiveness” or “spatial impression”
Reverberation time is a familiar auditorium characteristic
Though hard to quantify in a single measure, a fair indication of the “liveness”of a hall is given by the reverberation time of the mid frequencies (500 –2000 Hz)