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A Three-Parameter Broadband Model
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A simple model for the broadband impedance boundary condition is to take the resistance R to be a constant and the reactance X to be given by Eq. (10.2). That is,
where R0 > 0, X-1 < 0, X1 > 0.
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For this model, the time-domain impedance boundary condition may be written as follows:
It is straightforward to show, by assuming time dependence of the form e~imt for all variables, that Eq. (10.4) is equivalent to the frequency-domain impedance boundary condition with impedance given by Eq. (10.3).
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For a single-frequency sound field of frequency Q (Q > 0), this three-parameter model may still be used. Let Z0 = R0 – iX0 be the impedance of the acoustic liner at frequency Q, then the following choice of X-1 and X1 will transform the broadband model to a single-frequency model.
