Technology in Architecture

Lecture 13 Sound in Enclosed Spaces Reverberation Auditorium Design

Sound In Enclosed Spaces

Sound Absorption

Amount of sound energy not reflected S: p. 761, , F.18.2

Sound Absorption

Absorption coefficient α=I α /I i α=absorption coefficient I α =sound power intensity absorbed (w/cm 2 ) I i =sound power impinging on material (w/cm 2 ) 1.0 is total absorption

Sound Absorption

Absorption coefficient S: p. 759, T.18.1

Sound Absorption

Absorption A=Sα A=total absorption (sabins) S=surface area (ft 2 or m 2 ) α=absorption coefficient sabins (m 2 )= 10.76 sabins (sf)

Sound Absorption

Total Absorption Σα=S 1 α 1

+ S

2 α 2

+ S

3 α 3

+…+S

n α n or ΣA=A 1

+ A

2

+ A

3

+…+A

n

Sound Absorption

Average Absorption α avg =ΣA/S α avg <0.2 “live” α avg >0.4 “dead” S: p. 764, F.18.6

Reflection in enclosed spaces

Acoustical phenomena S: p. 777, F.18.20

S: p. 777, F.18.21

Ray diagrams

Trace the reflection paths to and from adjoining surfaces angle of incidence = angle of reflection I R

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

Reflection in enclosed spaces

Auditorium sound reinforcement S: p. 779, F.27.23

Reverberation

Reverberation

Persistence of sound after source has ceased S: p. 761, F.18.2

Reverberation Time

Period of time required for a 60 db drop after sound source stops T R

= K x V/ΣA

T R : reverberation time (seconds) K: 0.05 (English) (0.049 in SR-6) or 0.16 (metric) V: volume (ft 3 or m 3 ) ΣA: total room absorption, sabins (ft 2 or m 2 )

Reverberation Time

Application Volume 3.5

ft 3 x1000 35.0 350 S: p. 772, F.18.13

Reverberation Time

Calculated for “center band frequencies” 125 250 500 1000 2000 4000 Pay specific attention to 125 hz and 500 hz

Reverberation Example

Compile data

 

Material Absorption Coefficient Material Surface Area SR-6: p.121

Reverberation Example

Compare to requirements and adjust 3.5

ft 3 x1000 35.0 350 S: p. 772, F.27.13

Auditorium Design

Auditorium Design

Room Acoustics Noise Control Sound System

Auditorium Design Factors

Audience Size Range of Performance Activities Audience Sophistication

Auditorium Design Parameters

1. Audience Size (floor area): 6-8sf/seat 2. Reverberation (volume): Motion Picture Theatre Lecture Hall 100 cf/seat 100 cf/seat Music Room/Auditorium 200-250 cf/seat Symphony Hall 200-300 cf/seat Choral Rehearsal 350 cf/seat Band Rehearsal 500 cf/seat

Auditorium Design Parameters

3. Ceiling Height= Volume/Floor Area generally…20 x T R

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

Auditorium Design Parameters

5. Stage opening: 40-50’ wide x 25’ high

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 ceiling @ 40-60’ from stage 40’ 60’

Auditorium Design Parameters

7. Check Echoes

Auditorium Design Example

Given data RR-7: p.119

Reverberation Time

Symphonic 492,480 ft 3 3.5

ft 3 x1000 35.0 350 T R =1.5 seconds S: p. 772, F.18.13

Auditorium Design Example

Given data SR-6 : p.115, F.5-11

Auditorium Design Example

Given data SR-6 : p.116, F.5-12

Auditorium Design Example

Area takeoffs SR-6 : p.120

Auditorium Design Example

Locate coefficients S: p. 759, T.18.1

Auditorium Design Example

Absorption Coefficients SR-6 : p.121

Auditorium Design Example

Compute absorption Compute reverberation SR-6 : p.121

Auditorium Design Example

Compute T R 500 for given data: T R =0.049 x V/ ΣA =0.049 x 492,480/12,538 =1.92 seconds

Auditorium Design Example

Compute absorption needed for volume: T R =1.5 seconds ΣA=0.049 x V/T R =0.049 x 492,480/1.5

=16,088 sabins

Auditorium Design Example

Adjust to meet absorption Add acoustical tile on walls

Auditorium Design Example

Determine acoustical tile area

Auditorium Design Example

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

Auditorium Design Example

Add 5,299 sf of acoustical tile on walls Recompute T R500

Auditorium Design Example

Recompute T R-500 for revised data: T R-500 =0.049 x V/ ΣA =0.049 x 492,480/16,088 =1.5 seconds Compute T R-125 for revised data: T R-125 =0.049 x V/ ΣA =0.049 x 492,480/9,593 =2.52 seconds

Auditorium Design Example

Compare T R-500 with T R-125 : T R 125 /T R 500 =2.52/1.5= 1.68

Ratio should be 1.6-1.85

to offset hearing deficiency