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

4.1. ACOUSTIC TRANSMISSION BETWEEN TWO MEDIA 61By elimination of the reflected pressure wave p r from Equations 4.2 and 4.4we can find the ratio of the transmitted pressure to the normal incidentpressure :p a (0,t)p i (0,t) = 2z 2(4.6)z 2 +z 1From these last two equations we can calculate the coefficients of absorptionand reflection :a = I aI i= p2 az 2z 1p 2 iso :r = I rI i= p2 rz 1z 1p 2 ia = 4z 1z 2(z 1 +z 2 ) 2r = (z 2 −z 1 ) 2(z 1 +z 2 ) 2If the acoustic impedances z 1 and z 2 are frequency independent, so will be aand r, and they can be used for various waveforms.In practice, one can distinguish three cases :z l ≪ z 2 e.g. for the transition from gas to solid. In that case :a ≈ 4z 1z 2(4.7)and r ≈ 1, which means that only a small amount of energy will penetratethe solid and most energy will be reflected to the gas.z 1 = z 2 : Now a = 1, r = 0, which means that all energy incidenton the interface between two media, will be transmitted to the secondmedium. No energy will be reflected to the medium from which thewave is generated. This means that a so-called ’impedance match’ isrealized.z l ≫ z 2 (e.g. solid to gas). The same result is obtained as in the firstcase, because all the expressions of a and r are symmetrical in z 1 andz 2 . There is only small transition of acoustical energy and most energyis reflected.