THE SCIENCE AND APPLICATIONS OF ACOUSTICS - H. H. Arnold ...

282 12. Walls, Enclosures, and BarriersMost construction materials transmit only a small amount of acoustic energy,with the major portion of the energy undergoing reflection or conversion intoheat due to impedance mismatch, absorption within the material, and damping.Heavy walls, usually of masonry, allow very little of the sound to pass through,owing to their high mass per unit area. A wall of gypsum boards mounted onboth sides of a stud frame provides effective insulation against sound penetrationdue to energy losses resulting during the passage of sound from air to solid toair between the two panels to solid and thereon to air on the other side of thewall.A measure of sound insulation provided by a wall or some other structural barrieris given by the transmission loss TL, given in units of dB by( )W1TL = 10 log(12.1)W 2where W 1 represents the sound power incident on the wall and W 2 the sound powertransmitted through the wall. Because the frequency loss varies with the frequencyof the sound, it is usually listed for each octave band or one-third octave band. Thefraction of sound power transmitted through a wall or barrier constitutes the soundtransmission coefficient, τ, written asτ = W 2(12.2)W 1Combining Equations (12.1) and (12.2) we obtain( ) 1TL = 10 log(12.3)τorτ = 10 −TL/10 . (12.4)In Figure 12.1 we consider the case of a plane wave approaching a panel inthe y–z plane (i.e., the plane is normal to the x-axis) at an angle of incidence θ.Subscripts I , R, and T are used to identify, respectively, the incident wave, thereflected wave, and the transmitted wave. Arrows indicate the directions of thewave propagation. The wave equation for a plane wavebears the solutions:∂ 2 p∂t 2= c2 ∇ 2 pik(ct−x cos θ−y sin θ)p I = P I ep R = P R e ik(ct+x cos θ−y sin θ) . (12.5)ik(ct−x cos θ−y sin θ)p T = P T eHere the real part of p denotes the sound pressure, P, the (complex) pressureamplitude, and k, the wave number.