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Lecture 17Sound in Enclosed Spaces

ReverberationAuditorium Design

Lecture 17Sound in Enclosed Spaces

ReverberationAuditorium Design

Sound In Enclosed SpacesSound In Enclosed SpacesSound In Enclosed SpacesSound In Enclosed Spaces

Sound AbsorptionSound AbsorptionAmount of sound energy not reflected

S: p. 771, , F.18.2

Sound AbsorptionSound AbsorptionAbsorption coefficient

α=Iα/Ii

α=absorption coefficient Iα=sound power intensity absorbed (w/cm2)Ii=sound power impinging on material (w/cm2)

1.0 is total absorption

Sound AbsorptionSound AbsorptionAbsorption coefficient

S: p. 769, T.18.1

Sound AbsorptionSound Absorption

Absorption

A=Sα

A=total absorption (sabins)

S=surface area (ft2 or m2)α=absorption coefficient

sabins (m2)= 10.76 sabins (sf)

Sound AbsorptionSound Absorption

Total Absorption

Σα=S1α1 + S2α2 + S3α3 +…+Snαn

or

ΣA=A1 + A2 + A3 +…+An

Sound AbsorptionSound Absorption

Average Absorption

αavg=ΣA/S

αavg <0.2 “live”

αavg >0.4 “dead”

S: p. 774, F.18.6

Reflection in enclosed Reflection in enclosed spacesspaces

Acoustical phenomena

S: p. 787, F.18.20

S: p. 788, F.18.21

Ray diagramsRay diagrams

Trace the reflection paths to and from adjoining surfaces

angle of incidence = angle of reflection

I R

Ray diagramsRay 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 inReflection inenclosed spacesenclosed spaces

Auditorium sound reinforcement

S: p. 789, F.18.23

ReverberationReverberationReverberationReverberation

ReverberationReverberation

Persistence of sound after source has ceased

S: p. 771, F.18.2

Reverberation TimeReverberation 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)

Reverberation TimeReverberation Time

ApplicationVolume

S: p. 782, F.18.13

ft3x1000 3.5 35.0 350

Reverberation TimeReverberation Time

Calculated for “center band frequencies”

125 250 500 1000 2000 4000

Pay specific attention to 125 hz and 500 hz

Reverberation ExampleReverberation Example

Compile data Material Absorption

Coefficient Material Surface Area

SR-6: p.121

Reverberation ExampleReverberation Example

Compare to requirements and adjust

S: p. 782, F.27.13

ft3x1000 3.5 35.0 350

Auditorium DesignAuditorium DesignAuditorium DesignAuditorium Design

Auditorium DesignAuditorium Design

Room Acoustics

Noise Control Sound System

Auditorium Design FactorsAuditorium Design Factors

Audience SizeRange of Performance ActivitiesAudience Sophistication

Auditorium Design Auditorium Design ParametersParameters

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 200-250 cf/seat Symphony Hall 200-300 cf/seat Choral Rehearsal 350 cf/seat Band Rehearsal 500 cf/seat

Auditorium Design Auditorium Design ParametersParameters

3. Ceiling Height= Volume/Floor Area

generally…20 x TR

Auditorium Design Auditorium Design ParametersParameters

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 Auditorium Design ParametersParameters

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

Auditorium Design Auditorium Design ParametersParameters

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 Auditorium Design ParametersParameters

7. Check Echoes

Auditorium Auditorium Design Design ExampleExample

Given data

RR-7: p.119

Reverberation TimeReverberation Time

Symphonic492,480 ft3

TR=1.5 seconds

S: p. 782, F.18.13

ft3x1000 3.5 35.0 350

Auditorium Auditorium Design Design ExampleExample

Given data

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

Auditorium Auditorium Design Design ExampleExample

Given data

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

Auditorium Auditorium Design Design ExampleExample

Area takeoffs

SR-6: p.120

Auditorium Design ExampleAuditorium Design Example

Locate coefficients

S: p. 769, T.18.1

Auditorium Design ExampleAuditorium Design Example

Absorption Coefficients

SR-6: p.121

Auditorium Design ExampleAuditorium Design Example

Compute absorptionCompute reverberation

SR-6: p.121

Auditorium Design ExampleAuditorium Design Example

Compute TR 500 for given data:

TR=0.049 x V/ ΣA

=0.049 x 492,480/12,538 =1.92 seconds

Auditorium Design ExampleAuditorium 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

Auditorium Auditorium Design Design ExampleExample

Adjust to meet absorption

Add acoustical tile on walls

Auditorium Auditorium Design Design ExampleExample

Determineacousticaltile area

Auditorium Design ExampleAuditorium Design ExampleDetermine acoustical tile area

Sabins design 16,088- Sabins given 12,538 Sabins short 3,550

Translate to area of acoustical tile

Sabins/Δα=3,550/0.67= 5,299 sf

Auditorium Auditorium Design Design ExampleExample

Add 5,299 sfof acoustical tile on walls

RecomputeTR500

Auditorium Design ExampleAuditorium Design ExampleRecompute 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

Auditorium Design ExampleAuditorium Design Example

Compare TR-500 with TR-125 :

TR-125/TR-500=2.52/1.5= 1.68

Ratio should be 1.6-1.85to offset hearingdeficiency