an experimental evaluation of regular polyhedron loudspeakers as omnidirectional sources of sound...

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An Experimental An Experimental Evaluation Evaluation of Regular Polyhedron of Regular Polyhedron Loudspeakers Loudspeakers as Omnidirectional as Omnidirectional Sources of Sound Sources of Sound Sarah Rollins Sarah Rollins Timothy W. Leishman Timothy W. Leishman Acoustics Research Group Acoustics Research Group Department of Physics and Astronomy Department of Physics and Astronomy Brigham Young University Brigham Young University November 11, 2003 November 11, 2003

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Page 1: An Experimental Evaluation of Regular Polyhedron Loudspeakers as Omnidirectional Sources of Sound Sarah Rollins Timothy W. Leishman Acoustics Research

An Experimental An Experimental Evaluation Evaluation

of Regular Polyhedron of Regular Polyhedron LoudspeakersLoudspeakers

as Omnidirectional as Omnidirectional Sources of SoundSources of Sound

Sarah RollinsSarah RollinsTimothy W. LeishmanTimothy W. Leishman

Acoustics Research GroupAcoustics Research GroupDepartment of Physics and AstronomyDepartment of Physics and Astronomy

Brigham Young UniversityBrigham Young UniversityNovember 11, 2003November 11, 2003

Page 2: An Experimental Evaluation of Regular Polyhedron Loudspeakers as Omnidirectional Sources of Sound Sarah Rollins Timothy W. Leishman Acoustics Research

IntroductionIntroduction• Architectural AcousticsArchitectural Acoustics

• Omnidirectional sourceOmnidirectional source• Dodecahedron loudspeaker Dodecahedron loudspeaker

• Regular PolyhedronsRegular Polyhedrons

• Regular Polyhedron Loudspeakers (RPLs)Regular Polyhedron Loudspeakers (RPLs)• What about other RPLs besides the dodecahedron?What about other RPLs besides the dodecahedron?

Page 3: An Experimental Evaluation of Regular Polyhedron Loudspeakers as Omnidirectional Sources of Sound Sarah Rollins Timothy W. Leishman Acoustics Research

Regular Polyhedron Regular Polyhedron LoudspeakersLoudspeakers

• Built all 5 RPLsBuilt all 5 RPLs• 2 categories2 categories

• Equal Volume per Driver (EV)Equal Volume per Driver (EV)• Equal Midradii (EM)Equal Midradii (EM)

Page 4: An Experimental Evaluation of Regular Polyhedron Loudspeakers as Omnidirectional Sources of Sound Sarah Rollins Timothy W. Leishman Acoustics Research

Experimental SetupExperimental Setup

Page 5: An Experimental Evaluation of Regular Polyhedron Loudspeakers as Omnidirectional Sources of Sound Sarah Rollins Timothy W. Leishman Acoustics Research

Current StandardCurrent Standard

63 125 250 500 1000 2000 4000 8000-12

-8

-4

0

4

8

12

Frequency (Hz)

Dev

iatio

n (d

B)

ISO 3382-Equal Volume per Driver RPLs

ISO 3382 Tetrahedron Hexahedron Octahedron Dodecahedron Icosahedron

Page 6: An Experimental Evaluation of Regular Polyhedron Loudspeakers as Omnidirectional Sources of Sound Sarah Rollins Timothy W. Leishman Acoustics Research
Page 7: An Experimental Evaluation of Regular Polyhedron Loudspeakers as Omnidirectional Sources of Sound Sarah Rollins Timothy W. Leishman Acoustics Research
Page 8: An Experimental Evaluation of Regular Polyhedron Loudspeakers as Omnidirectional Sources of Sound Sarah Rollins Timothy W. Leishman Acoustics Research

Standard Deviation Standard Deviation FormulationFormulation

• Standard deviation of Standard deviation of directivity balloon directivity balloon valuesvalues

• Advantages over Advantages over current methodscurrent methods• VisualizationVisualization• Full sphere Full sphere

• DisadvantagesDisadvantages• More time consumingMore time consuming• More equipmentMore equipment

n

ii xx

n 1

2)(1

1

n

mmxn

x1

1

)log(102

Hx

Page 9: An Experimental Evaluation of Regular Polyhedron Loudspeakers as Omnidirectional Sources of Sound Sarah Rollins Timothy W. Leishman Acoustics Research

Standard Deviation PlotsStandard Deviation Plots

125 250 500 1000 2000 4000 80000

0.5

1

1.5

2

2.5

3

3.5

4

4.5

Frequency (Hz)

Sta

ndar

d D

evia

tion

(dB

)

(10log(|H|2))

TetrahedronEM HexahedronEV HexahedronEM OctahedronEV OctahedronEM DodecahedronEV DodecahedronIcosahedron

Page 10: An Experimental Evaluation of Regular Polyhedron Loudspeakers as Omnidirectional Sources of Sound Sarah Rollins Timothy W. Leishman Acoustics Research

Figure of Merit TableFigure of Merit Table

PPLPPL 4 kHz, σ(dB)4 kHz, σ(dB) 8 kHz, σ(dB)8 kHz, σ(dB)

TetrahedronTetrahedron *1.56*1.56 2.292.29

EM HexahedronEM Hexahedron 1.801.80 2.282.28

EV HexahedronEV Hexahedron 1.961.96 2.352.35

EM OctahedronEM Octahedron 2.032.03 2.442.44

EV OctahedronEV Octahedron 2.262.26 2.602.60

EM DodecahedronEM Dodecahedron 1.611.61 *2.19*2.19

EV DodecahedronEV Dodecahedron 1.991.99 2.322.32

IcosahedronIcosahedron 2.122.12 2.462.46

AverageAverage 1.921.92 2.372.37

* Indicates the lowest value for the given frequency range

Page 11: An Experimental Evaluation of Regular Polyhedron Loudspeakers as Omnidirectional Sources of Sound Sarah Rollins Timothy W. Leishman Acoustics Research

ConclusionsConclusions

• Best omnidirectional Best omnidirectional source source • Depends on bandwidthDepends on bandwidth

• TetrahedronTetrahedron• 0-4 kHz octave band0-4 kHz octave band• Contradicts ISO 3382Contradicts ISO 3382

• Dodecahedron Dodecahedron • 0-8 kHz octave band0-8 kHz octave band• More power outputMore power output

Page 12: An Experimental Evaluation of Regular Polyhedron Loudspeakers as Omnidirectional Sources of Sound Sarah Rollins Timothy W. Leishman Acoustics Research

Further ResearchFurther Research

• Higher resolution measurements Higher resolution measurements • High frequency informationHigh frequency information

• Impulse response measurementsImpulse response measurements• Compare measurements for different RPLs Compare measurements for different RPLs

and different orientationsand different orientations• Further comparison of standard Further comparison of standard

deviation with current methods to deviation with current methods to quantify omnidirectivityquantify omnidirectivity

• Analytical and numerical calculationsAnalytical and numerical calculations• Different size RPLsDifferent size RPLs

Page 13: An Experimental Evaluation of Regular Polyhedron Loudspeakers as Omnidirectional Sources of Sound Sarah Rollins Timothy W. Leishman Acoustics Research

AcknowledgmentsAcknowledgments

• Funding: NSF REU programFunding: NSF REU program• Advisor: Dr. Timothy W. LeishmanAdvisor: Dr. Timothy W. Leishman• Gordon DixGordon Dix• Kent GeeKent Gee• Todd KitchenTodd Kitchen• Wesley LifferthWesley Lifferth• Jacob RobinsonJacob Robinson