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62 CHAPTER 4. SOUND ABSORPTIONFigure 4.1: Transmission between two media.Example: interaction air/water: z 1 =415 rayl, z 2 = 1.48 × 10 6 rayl. Inthis case a = 0.00112 and r = 0.99888.Apparently the impedances are not adjusted and there is strong reflection.The fact that in Cases 1 and 3 there is mostly reflection, does not mean thatthe pressure waves form the same image in these two cases. We will nowconsider this. The total pressure in Medium 1 is given by :p(x,t) = Aexp(iωt−ikx)+Bexp(iωt+ikx) (4.8)with A and B are the amplitudes of the incident and reflected waves (noticethat thedirection ofpropagationof the reflected wave changes and that thereis a complex amplitude because a phase shift with respect to the referencemay occur). Again we distinguish two cases :Case 1 : (z 1 ≪ z 2 ) so B = A. This allows us to rewrite the pressure :p(x,t) = Aexp(iωt−ikx)+Aexp(iωt+ikx) = 2Acos(kx)cos(ωt)(4.9)This is a standing wave with amplitude 2Acos(kx). On the interfacex = 0, cos(kx) = 1andsotheamplitudeis2A. Therewillbeadoublingof pressure (also see Figure 4.2).Case 2 : (z 1 ≫ z 2 ) so B = −A. This allows us to rewrite the pressure :p(x,t) = Aexp(iωt−ikx)−Aexp(iωt+ikx) = 2Asin(kx)cos(ωt)(4.10)
4.1. ACOUSTIC TRANSMISSION BETWEEN TWO MEDIA 63This is a standing wave with amplitude 2Asin(kx). On the interfacex = 0, sin(kx) = 0, so the pressure is also equal to 0. (also see Figure4.3).Figure 4.2: Amplitude of the standing wave at transition from low to highimpedance.Figure 4.3: Amplitude of the standing wave at transition from high to lowimpedance.Fromtheabsorptionandreflectionexpressionsinfunctionoftheimpedances(see Equations 4.7), one can deduce that the impedance of a good acoustic
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VRIJE UNIVERSITEITBRUSSELAcousticsB
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iiWhen sound becomes noise, it will
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ContentsI Introduction to acoustics
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CONTENTSvii4.3 Measuring the acoust
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Part IIntroduction to acoustics1
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4 CHAPTER 1. FUNDAMENTAL CONCEPTS O
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10 CHAPTER 1. FUNDAMENTAL CONCEPTS
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6.3. TACKLING NOISE TRANSMISSION 11
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6.4. RADIATION NOISE 115Figure 6.17
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6.4. RADIATION NOISE 117Figure 6.20
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Part IIINoise directives119
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124CHAPTER 7. DIRECTIVE 2000/14/EG:
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128 CHAPTER 8. NOISE ON THE WORK FL
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140 CHAPTER 9. COMMUNITY NOISE2. No
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142 CHAPTER 9. COMMUNITY NOISE
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144 APPENDIX A. MATERIAL PROPERTIES
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152 BIBLIOGRAPHY[12] Bruel and Kjae
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