# Acoustic Resistance

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 (Pas/m3), or in the MKS system the rayl per square metre (rayl/m2), while that of specific acoustic impedance is the pascal-second per metre (Pas/m), or in the MKS system the rayl.[1] 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.

## acoustic resistance

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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:[citation needed]

Inductive acoustic reactance, denoted XL, and capacitive acoustic reactance, denoted XC, are the positive part and negative part of acoustic reactance respectively:[citation needed]

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. Acoustic reactance represents the pressure that is out of phase with the motion and causes no average energy transfer.[citation needed] 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.[citation needed] 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 time-invariant 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

Specific acoustic resistance, denoted r, and specific acoustic reactance, denoted x, are the real part and imaginary part of specific acoustic impedance respectively:[citation needed]

Specific inductive acoustic reactance, denoted xL, and specific capacitive acoustic reactance, denoted xC, are the positive part and negative part of specific acoustic reactance respectively:[citation needed]

Specific acoustic conductance, denoted g, and specific acoustic susceptance, denoted b, are the real part and imaginary part of specific acoustic admittance respectively:[citation needed]

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).[citation needed]

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:[citation needed]

The effect of acoustic impedance in medical ultrasound becomes noticeable at interfaces between different tissue types. The ability of an ultrasound wave to transfer from one tissue type to another depends on the difference in impedance of the two tissues. If the difference is large, then the sound is reflected. We grasp this intuitively at a macroscopic level. If you were to yell into a canyon, you would expect an echo to return to you. The sound wave in air meets the dense rocky canyon wall and reverberates off it back to you; the sound wave does not just pass into the rock. This is due to the difference in impedance 3.

where Zs is the source acoustic impedance, Ps is the source acoustic pressure, and Pmic is the sound pressure measured at the microphone in the ear canal. This study was completed with the approval of the Indiana University Institutional Review Board.

The circuit diagram for the model of the ear used in this study. The ear was modeled as a one-dimensional lossy transmission line (ear canal) terminated by a distributed load impedance, the middle ear and cochlea. This model is shown in a, with the two paths for the transmission line, a wave going in and a wave coming out, terminated by the load impedance. The line element for the transmission line is shown in b, consisting of a series impedance and a shunt admittance. The series impedance consists of resistance (R) and mass (M), the shunt admittance consists of conductance (G), and compliance (C). The resistance corresponds to viscous losses, the conductance to thermal losses, at the wall of the ear canal (Benade 1968). The load impedance, the middle ear and cochlea, is shown in c. The middle ear model incorporates the middle ear cavities (from Kringlebotn 1988), eardrum and ossicles, and cochlea. The eardrum and ossicles are represented by a bank of resonant filters, and the cochlea is represented by an RC circuit.

where a is the parameter in the nonlinear fitting of the model to the data that sets the final value of the radius, and ΥLF is the initial value for the radius. The initial value for the radius was the acoustic radius at low frequencies, given by:

where L is the acoustic length at the standing wave frequency (SWF), c is the velocity of sound, ρ is the density of air, ZLF is the acoustic input impedance of the ear at low frequencies, fi is the frequency, and n is the number of frequencies. fi ranged from 210 to 490 Hz.

R is the series (acoustical) resistance per unit length of the transmission line (viscous losses), M is the series inertance per unit length, G is the shunt conductance per unit length (thermal losses), C is the shunt compliance per unit length, and12

and d is the parameter in the nonlinear fitting of the model to the data that sets the scaling of viscous and thermal losses, P is the perimeter, and A is the cross-sectional area. P is not known and so d becomes a scaling factor that accounts for wall surface roughness, the boundary layer thickness (viscous and thermal) varying with the reciprocal of d. Keefe and Simmons (2003) included such a wall surface roughness factor in modeling calibration tube responses used to determine the acoustic output impedance of a sound source.

ei is the parameter in the nonlinear fitting of the model to the data that sets the resistance for the ith oscillator. pi is a parameter for the ith oscillator that is determined based on local maxima in the phase data (local resonances of the middle ear). pi is not a parameter that is free to vary in the fitting algorithm. Xk and Xm are given by:

This type of model captures well the acoustic input impedance of the middle ear. The circuit elements for the middle ear cavities and cochlea are from Kringlebotn (1988). A bank of resonant filters has been used previously by Zwislocki (1970) to represent the input impedance of the middle ear, in his mechanical coupler.

The fitting process consisted of three steps, middle ear resistance parameters found in the first step, ear canal and cochlear parameters found in the second step, and the scaling of viscothermal losses found in the third step. The process looped or repeated until, as described in the previous paragraph, initial and final values for each of the parameters differed by no more than 5 %. This approach restricted the number of parameters free to vary at each step to five, three, and one, respectively. With nine free parameters in total, this approach was used to avoid the local solutions which can arise with a large number of free parameters.

Figure 3 shows the rectangular co-ordinates, input resistance, and input reactance spectra, for the middle ear and cochlea. The three responses in each panel are (1) the model middle ear response from the model fit to data; (2) the data with the model-derived ear canal removed, i.e.,

In a previously published paper, a model for the nonlinear acoustic response of an area contraction including bias flow was presented. The model's prediction for the zero-driving resistance grew progressively worse as the steady-flow Mach number increased. This trend suggests that the forward loss coefficients should depend on the steady Mach number. This letter provides an empirical fitting of this Mach number dependence, along with additional validation data for the model. These additional validation data corroborate the model's prediction that the nonlinear impedance is frequency independent. This letter additionally provides an experimental methodology for determining the characteristic length with sample results.

Micro-perforated panels (MPPs) are widely used for broadband sound absorptions. For a MPP exposed to a grazing flow, existing acoustic impedance formulas based on different flow parameters give inconsistent results, thus calling for a systematic investigation of the issue to find more intrinsic flow parameters allowing for a reliable acoustic impedance prediction. In this study, three-dimensional CFD simulations are conducted on a MPP hole with a backing space in a flow duct. Numerical results allow identifying the flow velocity gradient in the viscous sublayer as the intrinsic flow parameter and show its linear relationship with a flow-related term in the acoustic resistance formula. Through a linear regression analysis, an acoustic resistance formula is established within a certain flow range (Mach number up to 0.25) under the linear acoustic regime. The validity of the impedance formula is demonstrated through comparisons with existing results and experimental data reported in the literature, showing good agreement and superiority in terms of the prediction accuracy. 041b061a72