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Concept
Acoustic impedance
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.
Official source
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