UNLV Retrospective Theses & Dissertations 1-1-1994 New empirical equations for calculating sound pressure levels in rooms Wen Bo Zeng University of Nevada, Las Vegas Follow this and additional works at: https://digitalscholarship.unlv.edu/rtds Repository Citation Zeng, Wen Bo, "New empirical equations for calculating sound pressure levels in rooms" (1994). UNLV Retrospective Theses & Dissertations. 399. http://dx.doi.org/10.25669/u24d-dw5z This Thesis is protected by copyright and/or related rights. It has been brought to you by Digital Scholarship@UNLV with permission from the rights-holder(s). You are free to use this Thesis in any way that is permitted by the copyright and related rights legislation that applies to your use. For other uses you need to obtain permission from the rights-holder(s) directly, unless additional rights are indicated by a Creative Commons license in the record and/ or on the work itself. 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Ann Arbor, MI 48106 NEW EMPIRICAL EQUATIONS FOR CALCULATING SOUND PRESSURE LEVELS IN ROOMS by Wen Bo Zeng A thesis submitted in partial fulfillment of the requirements for the degree of Master of Science in Mechanical Engineering Department of Mechanical Engineering University of Nevada, Las Vegas August 1994 © 1994 Wen Bo Zeng All Rights Reserved The Thesis of Wen Bo Zeng for the degree of Master of Science in Mechanical Engineering is approved. Chairperson, Dr. Douglas D. Reynolds W. Examining Committee Member, Dr. Darrell W. Pepper Examining Committee Member, Dr. Mohamed B. E. Trabia If: vH/ CM Graduate Faculty Representive, Dr. William G. Culbreth Dean of the Graduate College, Dr. Ronald W. Smith University of Nevada, Las Vegas August 1994 ABSTRACT Six room acoustic models were reviewed in the existing literature. There was no single acoustical model that was satisfactory for the rooms whose geometric and acoustic characteristics were different. In order to develop a new empirical room equation to predict the sound pressure distribution in rooms, seventeen rooms whose volumes ranged from 2,671 ft3 to 149,000 ft3 were examined. Two sets of sound tests, reverberation times and sound pressure levels, were conducted in these rooms. After a data base was built up, regression analyses were made. Finally, two empirical room acoustic equations, one for small rooms and another for large rooms, were developed from final regressions. These empirical room acoustic equations were simple, but with in acceptable accuracy. A graphical comparison with Schultz's equation” and field measured L - DL wasW also conducted. TABLE OF CONTENTS ABSTRACT ..................................................................................................... iii LIST OF TABLES ............................................................................................ vi LIST OF FIGURES ............................................................................................ vii LIST OF SYMBOLES .....................................................................................viii ACKNOWLEDGEMENTS............................................................................ ix CHAPTER I INTRODUCTION 1.1 Summary ............................................................................... 1 1.2 Introduction ......................................................................... 2 1.3 Literature Review ............................................................ 3 CHAPTER 2 MODELS 2.1 Point Sound Source Out In Space ................................. 9 2.2 The Diffuse Field T heory .............................................. 10 2.3 Modified Room Acoustic Equation .............................. 15 2.4 The Wave Acoustic Theory ........................................... 19 2.5 Computer M odel .............................................................. 24 2.6 Empirical Room Equation .............................................. 30 CHAPTER 3 MEASUREMENT PROCEDURE 3.1 Instrumentation ................................................................... 32 3.1.1 Norwegian Electronics Type 830 Real Time Analyzer ................................................................... 32 3.1.2 ACO Type 7046 Microphone .................................... 33 3.1.3 Acculab Reference Sound Source ............................... 33 3.1.4 Two-Way Hand Pum p ................................................. 33 3.1.5 Balloon .......................................................................... 35 3.1.6 XL33D Tape M easure ................................................. 35 3.2 Room Type And Characteristics ................................ 35 3.2.1 Room Size ........................................................................ 35 3.2.2 Room Characteristics .................................................... 37 3.3 T e s t...................................................................................... 38 3.3.1 Reverberation Time Measurement .............................. 39 3.3.2 Lp Measurement .............................................................. 41 3.3.3 LP - Lw Calculation .................................................... 42 CHAPTER 4 DEVELOPMENT OF EMPIRICAL EQUATIONS 4.1 Primary Regression .............................................................. 43 4.2 Final Regression ................................................................. 43 4.2.1 Empirical Equation For Small R oom s .......................44 4.2.2 Empirical Equation For Large R oom s ...................... 45 CHAPTER 5 DISCUSSION OF RESULTS 5.1 V ariables..................................................................................48 5.2 Schultz's Equation .............................................................. 49 5.3 Classic Equation ................................................................. 51 5.4 Equations Developed In This T hesis ...............................53 5.5 Deviations .............................................................................. 54 5.6 Recommendation For Lp - Lw Algorithm ................. 55 5.7 Simplification Of Equation 5 .7 ........................................ 56 5.8 Closing Comments ..............................................................57 CHAPTER 6 COCLUSIONS .....................................................................59 CHAPTER 7 FURTHER STUDY 7.1 Disproportional Rooms .....................................................61 7.2 Sound Source S iz e .............................................................. 61 REFERENCES................................................................................................. 63 APPENDIX A REVERBERATION TIMES ( s ) ..................................... 66 APPENDIX B LP - Lw DATA .....................................................................67 APPENDIX C REGRESSION DATA BASE ............................................75 APPENDIX D COMPUTER PROGRAMS.............................................. 79 APPENDIX E LP - Lw PLOTS ...................................................................100 v LIST OF TABLES Table 3-1 Average Sound Pressure Levels And Sound Power Levels O f Acculab R. S. S. - 101(0681) ............................................ 34 Table 3-2 Twelve Small Test R oom s ...................................................... 36 Table 3-3 Eight Large Test Rooms ......................................................... 36 Table 3-4 Sound Absorption Coefficients a Of The Rooms Examined In This T hesis ........................................................ 38 Table 5-1 Average Sound Absorption Coefficient, a, For typical Room Surfaces ..........................................................................