1. ROOM ACOUSTICS

2. THREE APPROACHES 1. GEOMETRIC RAY TRACING
2. RESONANCE (STANDING WAVES)
3. GROWTH AND DECAY OF SOUND

3. SIMPLE CONSTRUCTION OF SOUND RAYS WHICH OBEY THE LAWS OF REFLECTION
1. GEOMETRIC RAY TRACING
SIMPLE CONSTRUCTION OF SOUND RAYS WHICH OBEY THE LAWS OF REFLECTION 
THIS CAN BE USED TO INVESTIGATE.
THE DISTRIBUTION OF SOUND
EVENNESS/SHADOWS/FOCUSING
IMPROVE REFELECTIONS TO THE REAR OF THE SPACE
CHECK FOR THE POSSIBILITY OF ECHOES

4. SOUND DISTRIBUTION
Focus
Shadow
Weak
reflections

5. SEATING ARRANGEMENTS IS THERE DIRECT LINE OF SIGHT (AND HEARING!)
SLOPING SEATS / RAISED STAGE IMPROVE DIRECT SOUND
Sound attenuated by absorption of audience

6. USEFUL REFLECTIONS RECTANGULAR MODIFIED CEILING PROFILE
AREA OF USEFUL REFLECTION
RECTANGULAR
MODIFIED CEILING PROFILE
AREA OF USEFUL REFLECTION INCREASED

7. PROBLEMATIC REFLECTIONS
LONG (CUE BALL) REFLECTION WILL BE HEARD AS AN ECHO AT FRONT OF HALL (Delays of > 60ms)
CURE --- ADD REFLECTOR OR DIFFUSER (OR ABSORBER)
Echo
REFLECTOR
DIFFUSER

8. FLUTTER ECHOES
Sound “bounces” back and forth between the parallel reflective walls

9. Flutter Echo in a Small Theatre
View from stage
View from rear with reflective cinema screen
View from rear with reflective cinema screen covered with curtain

10. FIRST REFLECTION
The time delay between hearing the direct sound and the first reflection gives the listener an acoustic impression of the space.
Short delays make the space intimate (impression that there is a short distance between stage and audience)
Long delays make the audience feel remote from the “action”.
The acoustical measure of intimacy is called the initial time delay gap (ITDG) -- intimate if < 20 ms

11. Vertical surfaces give early reflections
short vertical walls provide early reflections to improve “acoustic intimacy” in a large space
Concert Hall - Vineyard Terrace Design

12. COMPUTER MODELS USE THE SAME TECHNIQUES TO BUILD UP A TIME HISTORY OF REFLECTED ENERGY

13. CONCERT HALL CEILING AND BALCONY REFLECTIONS

14. WALL REFLECTIONS

15. 2. RESONANCE (standing waves)
Sound can reflect back and forth in rooms
This can lead to standing waves at frequencies where the room dimension is a multiple of a wavelength
These waves are called ROOM MODES

16. Wave
plus
Reflection
Standing
wave =
Node Anti-node

18. ROOM MODES Axial Modes Tangential Modes Oblique Modes wall to wall
edge to edge
Oblique Modes
Corner to corner

19. EIGEN FREQUENCIES
The numbers NL, NW, NH are integers - 0,1, 2 etc. - which denotes the mode.
L, W & H are the room dimensions.
c is the speed of sound (340ms-1)
Modes 100, 010, 001, 200, etc are axial modes
Modes 110, 101, 011, 210, etc are tangential modes
Modes 111, 121, 211, etc are oblique modes
Evenly spaced modes are necessary for good acoustics in small rooms.

20. Example.
Find the first axial mode frequency along the length of a room 10m x 4m x 3m high.
Assume speed of sound in air = 340 ms-1
The length, L = 10m; width, W = 4m; height, H = 3m
NL = 1, NW = 0, NH = 0, axial mode along L.
If these are predicted from Hz a plot of modal density (number of modes per freq. band) can be drawn and the distribution of modes determined.

21. EFFECTS OF ROOM RESONANCE
ONLY A PROBLEM AT LOW FREQUENCIES AND SMALL ROOMS
GROUPED MODES GIVE COLOURATION AT LOW FREQUENCIES. (BOOMY BASS)
TRY SINGING IN THE BATHROOM (adds dynamic to voice)
CURES
USE GOLDEN RATIOS FOR ROOM DIMENSIONS
USE NON-PARALLEL WALLS
ADD ABSORPTION (DAMPING)

22. Ideal Room Proportions
Various proposals for ideal room proportions have been made. The enclosed area is the best-known, proposed by Bolt.
Red dots are particular ideal room proportions proposed by other authors.
Bolt, R. H. 1946, “Note on normal frequency statistics for rectangular rooms,” Journal of the Acoustical Society of America , 18,

23. 3. DECAY OF SOUND IN ROOMS
Wallace Clement Sabine was a pioneer in architectural acoustics
Over a century ago he started experiments in the Fogg lecture room at Harvard, to investigate the impact of absorption on the reverberation time.
He filled the room with sound using an organ pipe then switched it off and timed how long it took for the sound to become inaudible.
Later this was refined, the reverberation time was defined as the time taken for the sound to decay by 60 dB (to one millionth of the original intensity)

24. ROOM DECAY CURVE

25. Sabine Formula T = 0.161 V/A where T is the reverberation time (s)
V is the volume of the room (m3)
larger rooms have fewer reflection per second
A is the total absorption in the room (m2)
 areas x absorption coefficients
Other formulae (Eyring etc.) for dead rooms
T = V/A

26. EFFECT OF REVERBERATION ON SPEECH
CLEAR SEPARATE SYLLABLES
No Reverberation
Many factors influence speech intelligibility
T = 0.8 seconds
T = 1.5 seconds
T = 2.0 seconds
SYLLABLES MERGE TOGETHER MAKING SPEECH UNINTELLIGIBLE

27. RECOMMENDED REVERBERATION TIMES
Room volume (m3)
3.5
3.0
2.5
2.0
1.5
1.0
0.5
0.0
T (Secs)
CHURCH MUSIC
CONCERT HALLS
AUDITORIUM, SPEECH
TELEVISION STUDIO
Speech requires short RT --- to distinguish individual
consonants
Music requires longer RT --- blend, ensemble

28. REVERBERATON TIME INDICES
EDT(T10), T20, T30 are constructed from the slope over the first part of the decay given by the subscript.
(dB)
-10
-20
-30
-40
-50
-60
Noise off
0 dB
10 dB
20 dB
30 dB
(Seconds)
Decay curve
EDT (T10)
T30
T20

29. The RT will vary with position and time in complicated rooms
Three separate decays in a small church with balcony
Microphone is in the same position for each decay

30. REVERBERATION TIME MEASUREMENT (Interrupted Noise Method)
The time counting starts at time (1) when the level (4) is 5dB down from (2). The time counting goes on until (3), i.e. when the level has dropped to (5). It is important to specify a minimum distance to the noise floor which is (6).

31. DECAY CURVES ARE GENERALLY SMOOTHED
Old method using a chart recorder where the decay is drawn by a pen.
Selecting a slower pen speed smoothes out the decay
Current instruments use curve smoothing algorithms

32. REVERBERATION TIME MEASUREMENT (Impulse Excitation Method)
Back integration
Least squares fit
The curve is averaged over a number of decays.
A back integration technique developed by Schroeder smoothes the decay.
A least squares line is fitted and the 60 dB decay time found

33. USE OF ORCHESTRA AS SOUND SOURCE
Difficult to measure due to orchestra so use T10 or T15
I --- Early Decay of Instruments (perceived reverberation)
R --- Later Decay of Room

34. Objective measures for room acoustics
Reverberation
Clarity
Intimacy
Warmth and Brilliance
Loudness
Spaciousness
Background Noise

35. LINKS Room mode calculator http://www.mcsquared.com/metricmodes.htm
Behaviour of sound
Comparison of different hall shapes
Designing Auditoria