## Acoustics for Engineers: Troy LecturesThis book provides the material for an introductory course in engineering acoustics for students with basic knowledge in mathematics. It is based on extensive teaching experience at the university level. Under the guidance of an academic teacher it is su?cient as the sole te- book for the subject. Each chapter deals with a well de?ned topic and r- resents the material for a two-hour lecture. The chapters alternate between more theoretical and more application-oriented concepts. For the purpose of self-study, the reader is advised to use this text in parallel with further introductory material. Some suggestions to this end are given in Appendix 15. 3. The authors thank Dorea Ruggles for providing substantial stylistic re?- ments. Further thanks go to various colleagues and graduate students who most willingly helped with corrections and proof reading. Nevertheless, the authors assume full responsibility for all contents. Bochum and Troy, Jens Blauert February 2008 Ning Xiang Contents 1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1 1. 1 De?nition of Three Basic Terms . . . . . . . . . . . . . . . . . . . . . . . . . . . 1 1. 2 Specialized Areas within Acoustics . . . . . . . . . . . . . . . . . . . . . . . . . 3 1. 3 About the History of Acoustics . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4 1. 4 Relevant Quantities in Acoustics . . . . . . . . . . . . . . . . . . . . . . . . . . 5 1. 5 Some Numerical Examples . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6 1. 6 Levels and Logarithmic Frequency Intervals . . . . . . . . . . . . . . . . . 8 1. 7 Double-Logarithmic Plots . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10 2 Mechanic and Acoustic Oscillations . . . . . . . . . . . . . . . . . . . . . . . . 13 2. 1 Basic Elements of Linear, Oscillating, Mechanic Systems . . . . . 14 2. 2 Parallel Mechanic Oscillators . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 16 2. 3 Free Oscillations of Parallel Mechanic Oscillators . . . . . . . . . . . . 17 2. 4 Forced Oscillation of Parallel Mechanic Oscillators . . . . . . . . . . . |

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### Contents

1 | |

3 | |

4 | |

5 | |

6 | |

16 Levels and Logarithmic Frequency Intervals | 8 |

17 DoubleLogarithmic Plots | 10 |

Mechanic and Acoustic Oscillations | 12 |

81 Websters Dfferential Equation the Horn Equation | 104 |

82 Conical Horns | 105 |

83 Exponential Horns | 108 |

84 Radiation Impedances and Sound Radiation | 110 |

85 Steps in the Area Function | 111 |

86 Stepped Ducts | 113 |

Spherical Sound Sources and Line Arrays | 116 |

91 Spherical Sound Sources of 0th Order | 118 |

21 Basic Elements of Linear Oscillating Mechanic Systems | 14 |

22 Parallel Mechanic Oscillators | 16 |

23 Free Oscillations of Parallel Mechanic Oscillators | 17 |

24 Forced Oscillation of Parallel Mechanic Oscillators | 19 |

25 Energies and Dissipation Losses | 22 |

26 Basic Elements of Linear Oscillating Acoustic Systems | 24 |

27 The Helmholtz Resonator | 25 |

Electromechanic and Electroacoustic Analogies | 27 |

31 The Electromechanic Analogies | 28 |

32 The Electroacoustic Analogy | 29 |

34 Rules for Deriving Analogous Electric Circuits | 31 |

35 Synopsis of Electric Analogies of Simple Oscillators | 33 |

37 Examples of Mechanic and Acoustic Oscillators | 34 |

Electromechanic and Electroacoustic Transduction | 36 |

41 Electromechanic Couplers as Two or ThreePort Elements | 38 |

42 The Carbon Microphone A Controlled Coupler | 39 |

43 Fundamental Equations of Electroacoustic Transducers | 40 |

44 Reversibility | 43 |

45 Coupling of Electroacoustic Transducers to the Sound Field | 44 |

46 Pressure and PressureGradient Receivers | 46 |

47 Further Directional Characteristics | 49 |

48 Absolute Calibration of Transducers | 52 |

MagneticField Transducers | 55 |

51 The Magnetodynamic Transduction Principle | 57 |

52 Magnetodynamic Sound Emitters and Receivers | 59 |

53 The Electromagnetic Transduction Principle | 65 |

54 Electromagnetic Sound Emitters and Receivers | 67 |

55 The Magnetostrictive Transduction Principle | 68 |

56 Magnetostrictive Sound Transmitters and Receivers | 69 |

ElectricField Transducers | 70 |

62 Piezoelectric Sound Emitters and Receivers | 74 |

63 The Electrostrictive Transduction Principle | 78 |

64 Electrostrictive Sound Emitters and Receivers | 79 |

65 The Dielectric Transduction Principle | 80 |

66 Dielectric Sound Emitters and Receivers | 81 |

67 Further Transducer and Coupler Principles | 85 |

The Wave Equation in Fluids | 87 |

71 Derivation of the OneDimensional Wave Equation | 89 |

72 ThreeDimensional Wave Equation in Cartesian Coordinates | 93 |

73 Solutions of the Wave Equation | 95 |

74 Field Impedance and Power Transport in Plane Waves | 96 |

75 TransmissionLine Equations and Reflectance | 97 |

76 The Acoustic Measuring Tube | 99 |

Horns and Stepped Ducts | 103 |

92 Spherical Sound Sources of 1st Order | 122 |

93 HigherOrder Spherical Sound Sources | 124 |

94 Line Arrays of Monopoles | 125 |

95 Analogy to Fourier Transforms as Used in Signal Theory | 127 |

96 Directional Equivalence of Sound Emitters and Receivers | 130 |

Piston Membranes Diffraction and Scattering | 133 |

101 The Rayleigh Integral | 134 |

102 Fraunhofers Approximation | 135 |

103 The Far Field of Piston Membranes | 136 |

104 The Near Field of Piston Membranes | 138 |

105 General Remarks on Diffraction and Scattering | 142 |

Dissipation Reﬂection Refraction and Absorption | 145 |

111 Dissipation During Sound Propagation in Air | 147 |

112 Sound Propagation in Porous Media | 148 |

113 Reﬂection and Refraction | 151 |

114 Wall Impedance and Degree of Absorption | 152 |

115 Porous Absorbers | 155 |

116 Resonance Absorbers | 158 |

Geometric Acoustics and Diffuse Sound Fields | 161 |

121 Mirror Sound Sources and Ray Tracing | 162 |

122 Flutter Echoes | 165 |

123 Impulse Responses of Rectangular Rooms | 167 |

124 Diffuse Sound Fields | 169 |

125 ReverberationTime Formulae | 172 |

126 Application of Diffuse Sound Fields | 173 |

Isolation of Air and StructureBorne Sound | 177 |

132 Radiation of Airborne Sound by Bending Waves | 179 |

133 SoundTransmission Loss of SingleLeaf Walls | 181 |

134 SoundTransmission Loss of DoubleLeaf Walls | 184 |

135 The Weighted SoundReduction Index | 186 |

136 Isolation of Vibrations | 189 |

137 Isolation of Floors with Regard to Impact Sounds | 192 |

Noise Control A Survey | 194 |

141 Origins of Noise | 196 |

143 Noise Reduction as a System Problem | 200 |

144 Noise Reduction at the Source | 203 |

145 Noise Reduction Along the Propagation Paths | 204 |

146 Noise Reduction at the Receivers End | 208 |

Appendices | 211 |

152 Complex Notation for Power and Intensity | 212 |

214 | |

154 Letter Symbols Notations and Units | 215 |

219 | |

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### Common terms and phrases

absorbers acoustic air gap airborne sound analogies auditory baffle bending waves boundary called carbon microphone complex notation component constant couplers damping dashpot derived dielectric differential diffraction diffuse sound field Dirac impulse directional characteristics distance electret electric electric-field transducers Electroacoustic electromechanic electrostrictive elements Emitters and Receivers equivalent circuit example excitation field impedance force function Helmholtz resonator illustrates line array linear load loudspeakers magnetic Magnetostrictive mass material measured mechanic mechanic impedance medium microphones monopoles noise oscillator particle displacement particle velocity piezoelectric Piston Membranes plane wave porous quantities radiation impedance ratio reflection resonance reverberation schematically Section shown in Fig signal theory signals sinusoidal solution Sound Emitters sound incidence sound pressure sound propagation Spherical Sound Sources structure-borne sound term transducer transmission tube vibration voltage volume velocity wall wave equation wavelength Zwall