# Acoustic Impedance

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## Acoustic impedance

At a given surface, the complex ratio of effective sound pressure averaged over the surface to the effective flux (volume velocity or particle velocity multiplied by the surface area) through it. The unit is the N · s/m^{5} (newton-second/meter^{5}), or the mks acoustic ohm. In the cgs system the unit is the dyn · s/cm^{5} (dyne-second/centimeter^{5}). *See* Sound pressure

Specific acoustic impedance is the complex ratio of the effective sound pressure at a point to the effective particle velocity at a point. The unit is the N · s/m^{3}, or the mks rayl. In the cgs system the unit is the dyn · s/cm^{3}, or the rayl. The difference between specific acoustic impedance and acoustic impedance is in the specification of impedance at a point, as compared to the average over a surface.

Characteristic acoustic impedance is the ratio of effective sound pressure at a point to the particle velocity at that point in a free, progressive wave. This ratio is equal to the product of the density of the medium times the speed of sound in the medium. The characteristic impedance of a sound wave is analogous to the characteristic electrical impedance of an infinitely long, dissipationless transmission line. It is common in acoustical analyses to represent specific acoustic impedances in terms of their ratio to the characteristic impedance of air.

Acoustic impedance, being a complex quantity, can have real and imaginary components analogous to those in an electrical impedance. In applying this analogy, the real part of the acoustic impedance is termed acoustic resistance, and the imaginary part is termed acoustic reactance. *See* Electrical impedance

## Acoustic Impedance

a complex resistance that is introduced when examining the vibrations of acoustic systems, such as radiators, horns, and tubes. It is the ratio of the complex amplitudes of sound pressure to the volume vibratory velocity of the particles in a medium (the latter is equal to the product of the vibratory velocity averaged over an area and the area for which the acoustic impedance is being determined).

The complex expression for acoustic impedance has the form

*Z*_{a} = *R*_{a} + *iX*_{a}

where i = √ – 1is an imaginary unit. The resistive component R_{a} and the reactive component *X _{a}*, called the acoustic resistance and acoustic reactance, respectively, are obtained by separating acoustic impedance into real and imaginary parts. The resistive component is associated with friction and the energy losses caused by the sound radiation of an acoustic system; the reactive component is associated with the reactions of forces of inertia (masses) or elasticity (compliance).

In the SI system of units, acoustic impedance is measured in units of newton-seconds per m^{5} (N-sec/m^{5}); in the cgs system, in dyne-seconds per cm^{5} (dyne-sec/cm^{5}). (The designation “acoustic ohm” for this unit is encountered in the literature.) The concept of acoustic impedance is important in considering the propagation of sound in tubes of variable cross section and in horns or when discussing the acoustic properties of sound radiators and receivers and their cones and diaphragms. The power radiated by a system and its match to the medium are dependent on the acoustic impedance.

In addition to Z_{a}, the acoustic impedance, use is also made of the specific acoustic impedance and the mechanical impedance Z_{m} which are interrelated by the formula *Z _{m}* =

*SZ*

_{t}=

*S*

^{2}Z

_{a}, where

*S*is the area under consideration in the acoustic system. The specific acoustic impedance is expressed by the ratio of the sound pressure to the vibratory velocity at a given point or per unit area. In the case of a plane wave the specific acoustic impedance is equal to the characteristic impedance of the medium. The mechanical impedance (and the corresponding mechanical resistance and reactance) is defined as the ratio of the force (that is, the product of sound pressure and the area under consideration) to the average vibration velocity for the area. Theunit of mechanical impedance in the SI system is N-sec/m, andin the cgs system it is dyne • sec/cm (sometimes called the mechanical ohm).

I. G. RUSAKOV