Summary
Acoustic impedance and specific acoustic impedance are measures of the opposition that a system presents to the acoustic flow resulting from an acoustic pressure applied to the system. The SI unit of acoustic impedance is the pascal-second per cubic metre (), or in the MKS system the rayl per square metre (), while that of specific acoustic impedance is the pascal-second per metre (), or in the MKS system the rayl. There is a close analogy with electrical impedance, which measures the opposition that a system presents to the electric current resulting from a voltage applied to the system. For a linear time-invariant system, the relationship between the acoustic pressure applied to the system and the resulting acoustic volume flow rate through a surface perpendicular to the direction of that pressure at its point of application is given by: or equivalently by where p is the acoustic pressure; Q is the acoustic volume flow rate; is the convolution operator; R is the acoustic resistance in the time domain; G = R −1 is the acoustic conductance in the time domain (R −1 is the convolution inverse of R). Acoustic impedance, denoted Z, is the Laplace transform, or the Fourier transform, or the analytic representation of time domain acoustic resistance: where is the Laplace transform operator; is the Fourier transform operator; subscript "a" is the analytic representation operator; Q −1 is the convolution inverse of Q. Acoustic resistance, denoted R, and acoustic reactance, denoted X, are the real part and imaginary part of acoustic impedance respectively: where i is the imaginary unit; in Z(s), R(s) is not the Laplace transform of the time domain acoustic resistance R(t), Z(s) is; in Z(ω), R(ω) is not the Fourier transform of the time domain acoustic resistance R(t), Z(ω) is; in Z(t), R(t) is the time domain acoustic resistance and X(t) is the Hilbert transform of the time domain acoustic resistance R(t), according to the definition of the analytic representation.
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