1. Technology in Architecture
Lecture 17
Sound in Enclosed Spaces
Reverberation
Auditorium Design

2. Sound In Enclosed Spaces

3. Sound Absorption Amount of sound energy not reflected
S: p. 771, , F.18.2

4. Sound Absorption Absorption coefficient α=Iα/Ii
Iα=sound power intensity absorbed (w/cm2)
Ii=sound power impinging on material (w/cm2)
1.0 is total absorption

5. Sound Absorption
Absorption coefficient
S: p. 769, T.18.1

6. Sound Absorption Absorption A=Sα S=surface area (ft2 or m2)
A=total absorption (sabins)
S=surface area (ft2 or m2)
α=absorption coefficient
sabins (m2)= sabins (sf)

7. Sound Absorption Total Absorption Σα=S1α1 + S2α2 + S3α3 +…+Snαn or
ΣA=A1 + A2 + A3 +…+An

8. Sound Absorption Average Absorption αavg=ΣA/S αavg <0.2 “live”
αavg >0.4 “dead”
S: p. 774, F.18.6

9. Reflection in enclosed spaces
Acoustical phenomena
S: p. 787, F.18.20
S: p. 788, F.18.21

10. Ray diagrams Trace the reflection paths to and from adjoining surfaces
angle of incidence = angle of reflection I R

11. Ray diagrams Trace the reflection paths to receiver
Reflected sound path ≤ Direct sound path+55
Note: check rear wall
and vertical paths
Note: SR-6=RR-7
SR-6: p.116, F.5-12

12. Reflection in enclosed spaces
Auditorium sound reinforcement
S: p. 789, F.18.23

13. Reverberation

14. Reverberation Persistence of sound after source has ceased
S: p. 771, F.18.2

15. Reverberation Time
Period of time required for a 60 db drop after sound source stops
TR= K x V/ΣA
TR: reverberation time (seconds)
K: 0.05 (English) (0.049 in SR-6) or 0.16 (metric)
V: volume (ft3 or m3)
ΣA: total room absorption, sabins (ft2 or m2)

16. Reverberation Time Application Volume S: p. 782, F.18.13 ft3x1000
S: p. 782, F.18.13

17. Reverberation Time Calculated for “center band frequencies”
Pay specific attention to 125 hz and 500 hz

18. Reverberation Example
Compile data
Material Absorption Coefficient
Material Surface Area
SR-6: p.121

19. Reverberation Example
Compare to requirements and adjust
ft3x1000
S: p. 782, F.27.13

20. Auditorium Design

21. Noise Control Sound System
Auditorium Design
Room Acoustics
Noise Control Sound System

22. Auditorium Design Factors
Audience Size
Range of Performance Activities
Audience Sophistication

23. Auditorium Design Parameters
1. Audience Size (floor area): 6-8sf/seat
2. Reverberation (volume):
Motion Picture Theatre 100 cf/seat
Lecture Hall 100 cf/seat
Music Room/Auditorium cf/seat
Symphony Hall cf/seat
Choral Rehearsal 350 cf/seat
Band Rehearsal 500 cf/seat

24. Auditorium Design Parameters
3. Ceiling Height= Volume/Floor Area
generally…20 x TR

25. Auditorium Design Parameters
4. Typical Dimensions
L:W:H = 2H:1.5H:H
Determine acceptable width (80-120’)
Determine length (L = SF/Width)
If Length ≥120’, use balcony

26. Auditorium Design Parameters
5. Stage opening:
40-50’ wide x 25’ high

27. Auditorium Design Parameters
6. Shape Walls and Ceilings
a) source is 5’ from stage front, 5’ above stage floor
b) trace reflectances from back wall, side walls, and 40-60’ from stage
40’
60’

28. Auditorium Design Parameters
7. Check Echoes

29. Auditorium Design Example
Given data
RR-7: p.119

30. Reverberation Time Symphonic 492,480 ft3 TR=1.5 seconds
ft3x1000
S: p. 782, F.18.13

31. Auditorium Design Example
Given data
SR-6: p.115, F.5-11

32. Auditorium Design Example
Given data
SR-6: p.116, F.5-12

33. Auditorium Design Example
Area takeoffs
SR-6: p.120

34. Auditorium Design Example
Locate coefficients
S: p. 769, T.18.1

35. Auditorium Design Example
Absorption
Coefficients
SR-6: p.121

36. Auditorium Design Example
Compute absorption
Compute reverberation
SR-6: p.121

37. Auditorium Design Example
Compute TR 500 for given data:
TR=0.049 x V/ ΣA
=0.049 x 492,480/12,538
=1.92 seconds

38. Auditorium Design Example
Compute absorption needed for volume:
TR=1.5 seconds
ΣA=0.049 x V/TR
=0.049 x 492,480/1.5
=16,088 sabins

39. Auditorium Design Example
Adjust to
meet
absorption
Add
acoustical
tile on walls

40. Auditorium Design Example
Determine
acoustical
tile area

41. Auditorium Design Example
Determine acoustical tile area
Sabins design 16,088
- Sabins given 12,538
Sabins short ,550
Translate to area of acoustical tile
Sabins/Δα=3,550/0.67= 5,299 sf

42. Auditorium Design Example
Add 5,299 sf
of acoustical
tile on walls
Recompute
TR500

43. Auditorium Design Example
Recompute TR-500 for revised data:
TR-500=0.049 x V/ ΣA
=0.049 x 492,480/16,088
=1.5 seconds
Compute TR-125 for revised data:
TR-125=0.049 x V/ ΣA
=0.049 x 492,480/9,593
=2.52 seconds

44. Auditorium Design Example
Compare TR-500 with TR-125 :
TR-125/TR-500=2.52/1.5= 1.68
Ratio should be
to offset hearing
deficiency