Overview of Dr. L. L. Beranek\u27s 2006 paper on Analysis of Sabine and Eyring Equations and their Application to Concert Hall Audience and Chair Absorptio

Woods, Daniel C.

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Purdue UniversityPurdue e-PubsPublications of the Ray W. Herrick Laboratories School of Mechanical Engineering9-2014Overview of Dr. L. L. Beranek's 2006 paper onAnalysis of Sabine and Eyring Equations and theirApplication to Concert Hall Audience and ChairAbsorptionDaniel C. WoodsPurdue University, dcw.danielwoods@gmail.comFollow this and additional works at: https://docs.lib.purdue.edu/herrickThis document has been made available through Purdue e-Pubs, a service of the Purdue University Libraries. Please contact epubs@purdue.edu foradditional information.Woods, Daniel C., "Overview of Dr. L. L. Beranek's 2006 paper on Analysis of Sabine and Eyring Equations and their Application toConcert Hall Audience and Chair Absorption" (2014). Publications of the Ray W. Herrick Laboratories. Paper 194.https://docs.lib.purdue.edu/herrick/194NoiseCon 2014 September 8-10, 2014 Advancing the Technology and Practice of Noise Control Engineering Overview of Dr. L. L. Beranek's 2006 paper on  Analysis of Sabine and Eyring equations and their application  to concert hall audience and chair absorption   Daniel C. Woods  School of Mechanical Engineering and Ray W. Herrick Laboratories Purdue University West Lafayette, Indiana, USA  Introduction D. C. Woods Purdue University • Sabine and Eyring equations  • Predict reverberation times • Application to design of concert halls     1 Reverberant sound decay  (Backus, 19771) Tokyo Opera City Concert Hall2 Sabine Equation D. C. Woods Purdue University • Reverberation time directly related to enclosure volume, inversely related to amount of absorption 𝑇60 = 0.161 𝑉/(𝐴 + 4𝑚𝑉) [sec]     2 Sabine Equation D. C. Woods Purdue University • Reverberation time directly related to enclosure volume, inversely related to amount of absorption 𝑇60 = 0.161 𝑉/(𝐴 + 4𝑚𝑉) [sec]     Energy attenuation, sound traveling in air 2 Sabine Equation D. C. Woods Purdue University • Reverberation time directly related to enclosure volume, inversely related to amount of absorption 𝑇60 = 0.161 𝑉/(𝐴 + 4𝑚𝑉) [sec]     Total absorption  in room 2 𝐴 = α𝑠𝑎𝑏𝑆𝑡𝑜𝑡 Sabine Equation D. C. Woods Purdue University • Reverberation time directly related to enclosure volume, inversely related to amount of absorption 𝑇60 = 0.161 𝑉/(𝐴 + 4𝑚𝑉) [sec]     Total absorption  in room 2 Sabine absorption coefficients, 𝜶 α = 0 No absorption α → ∞ Complete absorption 𝐴 = α𝑠𝑎𝑏𝑆𝑡𝑜𝑡 Sabine Equation D. C. Woods Purdue University • Reverberation time directly related to enclosure volume, inversely related to amount of absorption 𝑇60 = 0.161 𝑉/(𝐴 + 4𝑚𝑉) [sec]     Total absorption  in room Acoustical area Sabine absorption coefficient (avg.) Audience/orchestra 𝑆𝑇  α𝑇  Highly absorbing surfaces 𝑆𝑖  α𝑖  Residual surfaces 𝑆𝑅 α𝑅 2 𝐴 = α𝑠𝑎𝑏𝑆𝑡𝑜𝑡 Eyring Equation D. C. Woods Purdue University • Alternate equation, predicts zero reverberation time for an absorption coefficient of 1 𝑇60 = 0.161 𝑉/(𝐴′ + 4𝑚𝑉) [sec]     3 Eyring Equation D. C. Woods Purdue University • Alternate equation, predicts zero reverberation time for an absorption coefficient of 1 𝑇60 = 0.161 𝑉/(𝐴′ + 4𝑚𝑉) [sec]     𝐴′ = −2.30 log10 1 − α𝑒𝑦 𝑆𝑡𝑜𝑡 3 Total absorption  in room Eyring Equation D. C. Woods Purdue University • Alternate equation, predicts zero reverberation time for an absorption coefficient of 1 𝑇60 = 0.161 𝑉/(𝐴′ + 4𝑚𝑉) [sec]     𝐴′ = −2.30 log10 1 − α𝑒𝑦 𝑆𝑡𝑜𝑡 Eyring absorption coefficients, 𝜶′ α′ = 0 No absorption α′ = 1 Complete absorption 3 Total absorption  in room Eyring Equation D. C. Woods Purdue University • Alternate equation, predicts zero reverberation time for an absorption coefficient of 1 𝑇60 = 0.161 𝑉/(𝐴′ + 4𝑚𝑉) [sec]     𝐴′ = −2.30 log10 1 − α𝑒𝑦 𝑆𝑡𝑜𝑡 3 Total absorption  in room Sabine absorption coefficient Eyring absorption coefficient Audience/orchestra α𝑇  α𝑇′ = α𝑒𝑦/α𝑠𝑎𝑏 α𝑇  Highly absorbing surfaces α𝑖  α𝑖′ = α𝑒𝑦/α𝑠𝑎𝑏 α𝑖  Residual surfaces α𝑅 α𝑅′ = α𝑒𝑦/α𝑠𝑎𝑏 α𝑅 Premise of the Paper D. C. Woods Purdue University • To predict reverberation times, absorption coefficients must be determined in spaces with similar locations of high absorption • Effective audience absorption coefficient varies with audience distribution     4 Premise of the Paper D. C. Woods Purdue University • To predict reverberation times, absorption coefficients must be determined in spaces with similar locations of high absorption    4 Boston Symphony Hall3 (contains upper areas where reverberation can develop) Manchester Bridgewater Hall4 (seats extend upward to impede overhead reverberation) Residual Absorption Coefficients D. C. Woods Purdue University • Measured or estimated from similar halls    5 Residual Absorption Coefficients D. C. Woods Purdue University • Measured or estimated from similar halls    5 New York Avery Fisher Hall5 Berlin Philharmonie Hall6  Rectangular Halls D. C. Woods Purdue University • Computed audience absorption coefficients, curves show averages for similar halls     6 Heavy upholstery Light to medium  upholstery Tokyo Opera City Rectangular Halls D. C. Woods Purdue University • Computed audience absorption coefficients, curves show averages for similar halls     6 Tokyo Opera City7  Tokyo Opera City Nonrectangular Halls D. C. Woods Purdue University • Audience absorption coefficients and unoccupied chair absorption coefficients   7 Audience absorption coefficients Chair absorption coefficients By upholstery: A–Heavy; B–Medium;         C–Light; D–Minimal Rectangular vs. Nonrectangular Halls D. C. Woods Purdue University 8 • Audience absorption coefficients for Sabine and Eyring equations  Conclusions D. C. Woods Purdue University 9 • Effective audience absorption coefficients are greater for: • Nonrectangular halls (compared to rectangular) • Heavier upholstery Conclusions D. C. Woods Purdue University 9 • Effective audience absorption coefficients are greater for: • Nonrectangular halls (compared to rectangular) • Heavier upholstery Greater volume needed Nonrectangular hall vs. rectangular ~6% Heavy upholstering vs. light/medium ~10% For same reverberation time  and audience size Conclusions D. C. Woods Purdue University 9 • Effective audience absorption coefficients are greater for: • Nonrectangular halls (compared to rectangular) • Heavier upholstery • To correctly predict reverberation times, absorption coefficients must be determined in spaces similar in: • Size and shape • Locations of high absorption (e.g. audience areas) • Reverberation times Acknowledgements D. C. Woods Purdue University  The author would like to thank Profs. J. Stuart Bolton, Patricia Davies, and Jeffrey Rhoads for their advice and support of this work 10 

Overview of Dr. L. L. Beranek\u27s 2006 paper on Analysis of Sabine and Eyring Equations and their Application to Concert Hall Audience and Chair Absorption

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Overview of Dr. L. L. Beranek\u27s 2006 paper on Analysis of Sabine and Eyring Equations and their Application to Concert Hall Audience and Chair Absorption

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