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16 CHAPTER 1. FUNDAMENTAL CONCEPTS OF ACOUSTICSFigure 1.3: Multiplication in the linear scale equals an addition in dB scalel.Source: Bruël&Kjær.1.5.3 Superposition of two soundsIn this section we will see in more detail how to superpose two sound waves.The resulting instantaneous pressure in a given point is the sum of the instantaneousvalues measured in that point : p(t) = p 1 (t)+p 2 (t). Due to thefactthat oneonlyhear andmeasure effective pressure values, thequestion is:what is the link between the effective pressures p total , p 1 en p 2 . This relationseems to depend on the nature of the sound and the distance between thesources. The total effective sound pressure is given by :√∫1 Tp eff = (p 1 (t)+p 2 (t)) 2 )dt=T√1T0∫ TTwo cases can be distinguished :0(p 2 1(t)+p 2 2(t)+2p 1 (t)p 2 (t))dtIncoherent sources One speak of incoherent sources if∫ T0(1.28)p 1 (t)p 2 (t)dt = 0 (1.29)
1.5. SOUND LEVELS 17InthiscasewecanthussaythatRMS(p total ) 2 = RMS(p 1 ) 2 +RMS(p 2 ) 2 .Examples of incoherent sources :two pure sine tones with differen ferquencies (e.g.two rotating machinesnot rotating synchronous)two independent stochastic soundstwo sources with energy in different frequency bandsSpecial case: iftwo coherent sourcesproducesoundpressure withsameamplitude we have p eff,1 = p eff,2 en dus p 2 eff,total = 2p 2 eff,1 , or in thedB scale :L p,total = L p,1 +3dB (1.30)The total sound pressure level is thus 3 dB higher compared to the caseof only one source present. And thus the noise is not twice as strong(an increase with factor two equals a rise of 6 dB).In general : for n independent sound sources we have that the effectivesound∑pressure in a given point equals the square root of p 2 eff,total =ni=1 p2 eff,i .Example : machines in an enterprise or cars in the street.In general : the n sources are independent but they cause the sameeffective pressure in a given point : p 2 eff,total = np2 eff,1 , or in dB scale :L p,total = L p,1 +10logn dBCoherent sources For coherent sources the following is valid :∫ T0p 1 (t)p 2 (t)dt ≠ 0 (1.31)In this case the total effective sound pressure depends on the phasedifference between the two single sound waves and the amplitudes.Suppose we have two sound waves p 1 en p 2 in a point x and defined asp 1 = Aexp(iωt) en p 2 = Aexp(iωt+φ) (for simplicity we consider thecase were the amplitudes of the waves are equal).One distinguish a few special cases :If φ = 0 we have that p 2 eff,total = 4p 2 eff,1 and for the dB value :L p,total = L p,1 +20logn dB (1.32)If φ = π than follows p 2 eff,total = 0. Considered apart p 1 andp 2 are audible, but together no sound is generated (ant-noise).
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5.3. THE ACOUSTICAL BARRIER 95For t
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Chapter 6Noise control6.1 Origin of
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6.1. ORIGIN OF NOISE 101Figure 6.2:
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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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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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