1. Auditorium acoustic (continued)
1. Sound sources in a room
Sound source can be characterized by power and directivity
Directivity factor Q – ratio of sound intensity in front of the source to the averaged sound intensity
For spherical source Q=1, for hemispherical Q=2, for source in a corner (which radiates into one-quarter of a sphere) Q=4
Intensity drop as:
Intensity level:

2. r 2. Sound sources in a room
The distribution of sound level in a room can be considered as a sound field
Three regions in a sound field:
Near field - distance from the source is small compared to dimensions of the source. Intensity varies with location and depends on the type of the source.
Free field – intensity drops as 1/r2 (r is distance from the source). Intensity level drops 6dB when distance r doubles
Reverberant field – region where reflected sound becomes important r
Reverberant field
Near field
Free field

3. The shown temperatures are samples of a field77 82 83 68 55 66 75 80 90 91 71 72 84 73 88 92 64

4. 2. The Bass Loss Problem
When sound drops off according to the inverse square law, the sound further from the source is not only perceived as less loud but also as deficient in the bass frequencies. This is a natural result of the human hearing response as revealed by the equal loudness curves. There is a bass discrimination in the human hearing response for soft sounds.

5. Equal Loudness Curves
Phon is equal to the sound pressure level in decibels at f = 1 kHz
30 Hz: dB ~ 80 phons; ( ) dB = 83 dB ~ 50 phons
200Hz: dB ~ 80 phons; (76 -20) dB = 56 dB ~ 60 phons

6. 2. Loudspeaker placemat
A. Single-source system
Preferred in most auditoriums.
Generally consists of a cluster of loudspeakers with selected directivity factors Q.
Preferred location in the center of the room, over the speaker head.
(Vertical displacement of the source is not distracting becaus of our inability to localize sound in a vertical plane.)
Aimed toward the listeners at the rear of the auditorium.
B. Distributed-speaker system
Useful for long room with low ceiling.
Each unit mounted in the ceiling covers 60◦ - 90◦
If room is long it is important to have electronic time delay for rear speakers to avoid echo.
Speakers should not be placed along the side walls because some listeners will hear sound from several loudspeakers at the same time
Speakers should not be placed on each side of the stage or front wall, because some listeners will hear sound from one of the speakers before they hear the direct sound.

7. Acoustic diffusers are used to maintain the acoustic energy in a room, but at the same time removing strong echoes.
Acoustic diffusion occurs in a haphazard (irregular) way in many historical buildings through the use of ornate wall decorations and statues.
Modern rooms rarely have such decorations but may include curved walls or other architectural features to achieve some of the same effect