VRIJE UNIVERSITEIT BRUSSEL Acoustics - the Dept. of ...

78 CHAPTER 4. SOUND ABSORPTIONBecause ρcW 0p 2 0≈ 1 for air, we can write :L p = L W −10logA+6dB (4.34)This way, one can determine the sound level of a given sound source ifthe absorption of the room and the sound power is known.Two different sound fields with a different propagation behavior exist :the diffuse field and the direct field. In the diffuse field the pressure is uniformthroughout the field (the propagation direction in any point is randomuniform). The diffuse field does not extend over the space, but is only validfrom a certain distance from the sound source. Close to the source a directfield is present (propagation in one direction and SPL highly dependent onthe distance to the source). For a point source in a free field the followingexpression holds (see Chapter 1) :p 2 = ρcW4πr 2 (4.35)Now, both direct and diffuse fields occur together in a space, so we haveto add the different contributions to the pressure. This is done by using theexpression for adding non-coherent sources :p 2 total = p2 direct +p2 diffuse (4.36)and thus :or in dB scale (for air) :( 1p 2 total = ρcW 4πr + 4 )2 A( 1L p = L W +10log4πr + 4 )2 A(4.37)(4.38)ThegraphofL p fordifferent valuesofthetotalabsorptonAisgiveninFigure4.10.Conclusion : at a certain distance from the source, the sound field isamplified because of the reflections which are due to the partial absorptionof the walls.The seperation between the direct free field and the diffuse field is givenby a value R of r for which both fields produce an equal sound pressure.This value R is called the reverberation radius. For the determination of thereverberation radius we write :ρcW4πR = 4ρcW2 A(4.39)