Mathematical acoustic impedance

For planar layers, analjftic equations predicting A/ and AF from the model parameters (layer thickness, storage modulus, loss modulus) exist. Mathematical details of modeling have been provided in a recent book chapter. The models basically amount to a prediction of the acoustic reflectivity of the resonator t sample interface. For planar layers, this reflectivity is calculated in essentially the same way as in optics. The role of the refractive index is taken by the material s acoustic impedance, Zac =... 

However, the length of the sample, if it is comparable to the length of the acoustic waves can cause wave interference effects to arise at the sample-water interface and these must be taken into account in a theoretical description. The mathematical treatment of these effects can be found in the literature of transmission line theory which provides the following expression for the impedance of a length 1 of material... 

If, however, we are interested in the high-frequency behavior of the column, then we must treat the impedance as that of an RC chain as shown in Figure 17.16. Here each RC section represents one tray, the resistance is that of the tray and layer of liquid to vapor flow, and the capacitance is the acoustic capacitance of the space between the trays. The terminal impedance, Zj s), is simply P s)/Qc s)- Mathematically the entire network may be studied by the methods of transmission-line analysis. 

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