ALTERNATIVE METHODS FOR ASSESSING THE OMNIDIRECTIONALITY OF SOURCES FOR ROOM ACOUSTICS MEASUREMENTS

Transcription

1 ALTERNATIVE METHODS FOR ASSESSING THE OMNIDIRECTIONALITY OF SOURCES FOR ROOM ACOUSTICS MEASUREMENTS Timothy W. Leishman Research Group Department of Physics and Astronomy Brigham Young University 150th Meeting of the Acoustical Society of America October 21, 2005

2 A Few Definitions P An omnidirectional acoustic source radiates sound equally in all directions. It is an ideal for many architectural acoustics measurements. P A unidirectional acoustic source (predominantly) radiates sound in only one direction. P A multidirectional source predominantly radiates sound in various directions. Its behavior is somewhere between that of a unidirectional source and that of an omnidirectional source.

3 INTRODUCTION Background P Acousticians frequently use multiple-driver loudspeakers as omnidirectional sources in room acoustics measurements. P Omnidirectional source qualification procedures are outlined in ISO and ISO P Regular polyhedron loudspeakers (RPLs) (particularly dodecahedrons) have been widely accepted and are recommended in the standards. P RPL adoption was strengthened by Tarnow in P RPLs are nearly omnidirectional up to about 1 khz, but become multidirectional at higher frequencies. P Other source configurations are also possible.

4 Motivations P Presumably omnidirectional sources exhibit unprescribed and undesirable directivities at many frequencies of interest. P How can one easily and accurately determine the omnidirectivity of a source? P Qualification of omnidirectional sources is basically fudged in ISO standards: < Gliding averages over measurement arcs (spatial averaging). < Broad proportional frequency bands (spectral averaging). < Pink noise weights lower portions of bands. < Only a single measurement plane required. < Omnidirectivity requirements relaxed at higher frequencies. < No omnidirectivity requirements above 5.6 khz. P Preliminary work revealed discrepancies with ISO qualification results.

5 ISO 3382 Results for Several RPLs ISO 3382 Limits Tetrahedron Hexahedron Octahedron Dodecahedron Icosahedron Frequency (Hz)

6 P Current standards do not challenge manufacturers to develop better omnidirectional sources. P Should the ISO source qualification procedures be revisited?

7 Research Objectives P Investigate several alternative methods for assessing source omnidirectivity. P Explore strengths, weaknesses, and discrepancies of the various methods. P Propose solid practical alternatives to the source qualification procedures outlined in the ISO standards.

8 METHODS Constructed RPLs

9 Free-Field Measurements

10 Radiated Field Sampling P 2664 narrow-band FRFs. < Smooth frequency dependence. < Postprocessing ability. P Sampling areas: S S p = mn θ 4π r = 2r = φ = 5 r = 2.1 m sin φ sin( θ ) θ 4 θ m sin 2

11 Frequency-Dependent Directivity Animation for a Dodecahedron Loudspeaker

12 Narrow-Band vs. Octave-Band Directivity 2 khz 4 khz 8 khz NB OB

13 Alternative Omnidirectionality Assessments (Thus Far) P Area-weighted arithmetic or energetic average of normalized levels. P Area-weighted arithmetic or energetic standard deviation of levels. < Related to work on scattering uniformity or diffusion. < Linear perceptual scale. P Area-weighted arithmetic or energetic average of normalized spatially dependent directivity indices. P Area-weighted arithmetic or energetic standard deviation of spatially dependent directivity indices. P Sound pressure level spectrum at one or more measurement positions after source sound power equalization.

14 Top Contenders (Thus Far) P Area-weighted arithmetic (or energetic) average of normalized levels: L m, n ( f ) S M 1N 1 M 1N 1 S L ( f ) m, n m, n m= 0 n= 0 = M 1N 1 m= 0 n= 0 P Area-weighted arithmetic (or energetic) standard deviation of levels: S m, n [ ( ) ( ) ] S L f L f m, n m, n m, n S m= 0 n= 0 σ AWL ( f ) = M 1N 1 m= 0 n= 0 S m, n 2

15 RESULTS

16 Area-Weighted Arithmetic and Energetic Averages of Normalized Levels Arithmetic Energetic k 10 k Frequency (Hz)

17 Narrow and Third-Octave Band Area-Weighted Arithmetic Average of Normalized Levels Third Octave Narrow Band k 10 k Frequency (Hz)

18 Narrow and Third-Octave Band Area-Weighted Arithmetic Standard Deviation of Levels 3 Third Octave Narrow Band k 10 k Frequency (Hz)

19 Modified Averages of Normalized Levels and Standard Deviation of Levels 8 6 Arithmetic Average Energetic Average Standard Deviation k 10 k Frequency (Hz)

20 Simplified Sampling Schemes (Single Planes)

21 Third-Octave Area-Weighted Arithmetic Average of Normalized Levels: Full Sphere vs. Full Equator Full Sphere Full Equator k 10 k Frequency (Hz)

22 Third-Octave Area-Weighted Arithmetic Standard Deviation of Levels: Full Sphere vs. Half Meridian 3 Full Sphere Half Meridian k 10 k Frequency (Hz) 0.5

23 CONCLUSIONS P Alternative methods have been and are continuing to be explored to assess the omnidirectionality of sources for room acoustics measurements. P Average normalized level and standard deviation methods show promise and very similar trends, but do not always agree with the ISO qualification method. P The average normalized level and standard deviation methods provide global views of omnidirectional behavior. P The methods may also be applied with fewer measurement points on single planes with limited but reasonable accuracy. P Of the two methods, the standard deviation method appears to provide better results for a single measurement plane.

24 P The two methods may be used with proportional bands. P However, full-octave bands are not recommended because of their excessive directivity averaging at higher frequencies. P These methods may be used to complement the current ISO source qualification methods. P Future work: < Testing and comparison of additional metrics. < Determination of the best metric for assessing omnidirectivity of sources. < Development of single-number omnidirectivity coefficients. < Development of practical methods for assessing omnidirectivity. < Error analysis.