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Sound measurements  

Characteristic  Symbols 
Sound pressure  p, SPL,L_{PA} 
Particle velocity  v, SVL 
Particle displacement  ? 
Sound intensity  I, SIL 
Sound power  P, SWL, L_{WA} 
Sound energy  W 
Sound energy density  w 
Sound exposure  E, SEL 
Acoustic impedance  Z 
Audio frequency  AF 
Transmission loss  TL 
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 the rayl per square metre , while that of specific acoustic impedance is the pascal second per metre or the rayl.^{[1]} In this article the symbol rayl denotes the MKS rayl. There is a close analogy with electrical impedance, which measures the opposition that a system presents to the electrical flow resulting from an electrical voltage applied to the system.
For a linear timeinvariant 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
Acoustic impedance, denoted Z, is the Laplace transform, or the Fourier transform, or the analytic representation of time domain acoustic resistance:^{[1]}
where
Acoustic resistance, denoted R, and acoustic reactance, denoted X, are the real part and imaginary part of acoustic impedance respectively:^{[]}
where
Inductive acoustic reactance, denoted X_{L}, and capacitive acoustic reactance, denoted X_{C}, are the positive part and negative part of acoustic reactance respectively:^{[]}
Acoustic admittance, denoted Y, is the Laplace transform, or the Fourier transform, or the analytic representation of time domain acoustic conductance:^{[1]}
where
Acoustic conductance, denoted G, and acoustic susceptance, denoted B, are the real part and imaginary part of acoustic admittance respectively:^{[]}
where
Acoustic resistance represents the energy transfer of an acoustic wave. The pressure and motion are in phase, so work is done on the medium ahead of the wave; as well, it represents the pressure that is out of phase with the motion and causes no average energy transfer.^{[]} For example, a closed bulb connected to an organ pipe will have air moving into it and pressure, but they are out of phase so no net energy is transmitted into it. While the pressure rises, air moves in, and while it falls, it moves out, but the average pressure when the air moves in is the same as that when it moves out, so the power flows back and forth but with no time averaged energy transfer.^{[]} A further electrical analogy is a capacitor connected across a power line: current flows through the capacitor but it is out of phase with the voltage, so no net power is transmitted into it.
For a linear timeinvariant system, the relationship between the acoustic pressure applied to the system and the resulting particle velocity in the direction of that pressure at its point of application is given by
or equivalently by:
where
Specific acoustic impedance, denoted z is the Laplace transform, or the Fourier transform, or the analytic representation of time domain specific acoustic resistance:^{[1]}
where v^{ 1} is the convolution inverse of v.
Specific acoustic resistance, denoted r, and specific acoustic reactance, denoted x, are the real part and imaginary part of specific acoustic impedance respectively:^{[]}
where
Specific inductive acoustic reactance, denoted x_{L}, and specific capacitive acoustic reactance, denoted x_{C}, are the positive part and negative part of specific acoustic reactance respectively:^{[]}
Specific acoustic admittance, denoted y, is the Laplace transform, or the Fourier transform, or the analytic representation of time domain specific acoustic conductance:^{[1]}
where
Specific acoustic conductance, denoted g, and specific acoustic susceptance, denoted b, are the real part and imaginary part of specific acoustic admittance respectively:^{[]}
where
Specific acoustic impedance z is an intensive property of a particular medium (e.g., the z of air or water can be specified); on the other hand, acoustic impedance Z is an extensive property of a particular medium and geometry (e.g., the Z of a particular duct filled with air can be specified).^{[]}
For a one dimensional wave passing through an aperture with area A, the acoustic volume flow rate Q is the volume of medium passing per second through the aperture; if the acoustic flow moves a distance dx = v dt, then the volume of medium passing through is dV = A dx, so:^{[]}
Provided that the wave is only onedimensional, it yields
The constitutive law of nondispersive linear acoustics in one dimension gives a relation between stress and strain:^{[1]}
where
This equation is valid both for fluids and solids. In
Newton's second law applied locally in the medium gives:^{[]}
Combining this equation with the previous one yields the onedimensional wave equation:
The plane waves
that are solutions of this wave equation are composed of the sum of two progressive plane waves traveling along x with the same speed and in opposite ways:^{[]}
from which can be derived
For progressive plane waves:^{[]}
or
Finally, the specific acoustic impedance z is
The absolute value of this specific acoustic impedance is often called characteristic specific acoustic impedance and denoted z_{0}:^{[1]}
The equations also show that
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Temperature acts on speed of sound and mass density and thus on specific acoustic impedance.
Temperature T (°C) 
Speed of sound c (m/s) 
Density of air ? (kg/m^{3}) 
Characteristic specific acoustic impedance z_{0} (Pa·s/m) 

35  351.88  1.1455  403.2 
30  349.02  1.1644  406.5 
25  346.13  1.1839  409.4 
20  343.21  1.2041  413.3 
15  340.27  1.2250  416.9 
10  337.31  1.2466  420.5 
5  334.32  1.2690  424.3 
0  331.30  1.2922  428.0 
5  328.25  1.3163  432.1 
10  325.18  1.3413  436.1 
15  322.07  1.3673  440.3 
20  318.94  1.3943  444.6 
25  315.77  1.4224  449.1 
For a one dimensional wave passing through an aperture with area A, Z = z/A, so if the wave is a progressive plane wave, then:^{[]}
The absolute value of this acoustic impedance is often called characteristic acoustic impedance and denoted Z_{0}:^{[1]}
and the characteristic specific acoustic impedance is
If the aperture with area A is the start of a pipe and a plane wave is sent into the pipe, the wave passing through the aperture is a progressive plane wave in the absence of reflections, and the usually reflections from the other end of the pipe, whether open or closed, are the sum of waves travelling from one end to the other.^{[]} (It is possible to have no reflections when the pipe is very long, because of the long time taken for the reflected waves to return, and their attenuation through losses at the pipe wall.^{[]}) Such reflections and resultant standing waves are very important in the design and operation of musical wind instruments.^{[]}