The acoustic impedance Z (or sound impedance) is a frequency f dependent parameter and is very useful, for example, for describing the behaviour of musical wind instruments. Mathematically, it is the sound pressure p divided by the particle velocity v divided by the surface area S through which an acoustic wave of frequency f propagates. If the impedance is calculated for a range of excitation frequencies the result is an impedance curve. Plane, single-frequency traveling waves have acoustic impedance equal to the characteristic impedance, the product of longitudinal wave velocity and density of the medium divided by the surface area. Acoustic impedance can be expressed in either its constituent units (pressure per velocity per area) or in rayls. // Sound pressure Sound pressure is the pressure deviation from the local ambient pressure caused by a sound wave. ... It has been suggested that this article or section be merged into Sound pressure. ... Particle velocity is the velocity v of a particle (real or imagined) in a medium as it transmits a wave. ... The particle velocity level or the sound velocity level tells the ratio of a sound incidence in comparison to a reference level of 0 dB. It shows the ratio of the particle velocity v1 and the particle velocity v0. ... Particle displacement or particle amplitude (represented in mathematics by the lower-case Greek letter ξ) is a measurement of distance (in metres) of the movement of a particle in a medium as it transmits a wave. ... The sound intensity, I, (acoustic intensity) is defined as the sound power Pac per unit area A. The usual context is the noise measurement of sound intensity in the air at a listeners location. ... Sound intensity level or acoustic intensity level is a logarithmic measure of the sound intensity in comparison to the reference level of 0 dB (decibels). ... Sound power or acoustic power Pac is a measure of sonic energy E per time t unit. ... Sound power level or acoustic power level is a logarithmic measure of the sound power in comparison to a specified reference level. ... The sound energy density or sound density (symbol E or w) is an adequate measure to describe the sound field at a given point as a sound energy value. ... The sound energy flux is the average rate of flow of sound energy for one period through any specified area. ... Sound is a vibration that travels through an elastic medium as a wave. ... // Sound pressure Sound pressure is the pressure deviation from the local ambient pressure caused by a sound wave. ... Particle velocity is the velocity v of a particle (real or imagined) in a medium as it transmits a wave. ... A wave is a disturbance that propagates through space or spacetime, often transferring energy. ... Longitudinal waves are waves that have vibrations along or parallel to their direction of travel. ... In physics, density is mass m per unit volume V. For the common case of a homogeneous substance, it is expressed as: where, in SI units: ρ (rho) is the density of the substance, measured in kg·m-3 m is the mass of the substance, measured in kg V is... A rayl is one of two units of acoustic impedance. ...

Note that sometimes vS is referred to as the volume velocity.

The specific acoustic impedance z is the ratio of sound pressure p to particle velocity v at a single frequency. Therefore // Sound pressure Sound pressure is the pressure deviation from the local ambient pressure caused by a sound wave. ... Particle velocity is the velocity v of a particle (real or imagined) in a medium as it transmits a wave. ...

Distinction has to be made between:

• the characteristic acoustic impedance Z₀ of a medium, usually air (compare with characteristic impedance in transmission lines).
• the impedance Z of an acoustic component, like a wave conductor, a resonance chamber, a muffler or an organ pipe.

The characteristic impedance of a uniform transmission line is the ratio of the amplitudes of a single pair of voltage and current waves propagating along the line in the absence of reflections. ... A transmission line is the material medium or structure that forms all or part of a path from one place to another for directing the transmission of energy, such as electromagnetic waves or acoustic waves, as well as electric power transmission. ...

Characteristic impedance

The characteristic impedance of a medium, such as air, rock or water is a material property: Layers of Atmosphere - not to scale (NOAA)[3] Earths atmosphere is a layer of gases surrounding the planet Earth and retained by the Earths gravity. ... Standard atmosphere (symbol: atm) is a unit of pressure. ... Celsius is, or relates to, the Celsius temperature scale (previously known as the centigrade scale). ... This article does not cite any references or sources. ... In physics, density is mass m per unit volume V. For the common case of a homogeneous substance, it is expressed as: where, in SI units: ρ (rho) is the density of the substance, measured in kg·m-3 m is the mass of the substance, measured in kg V is... The pascal (symbol: Pa) is the SI derived unit of pressure or stress (also: Youngs modulus and tensile strength). ... Layers of Atmosphere - not to scale (NOAA)[3] Earths atmosphere is a layer of gases surrounding the planet Earth and retained by the Earths gravity. ... The rocky side of a mountain creek near Orosí, Costa Rica. ... Impact from a water drop causes an upward rebound jet surrounded by circular capillary waves. ...

where

Z₀ is the characteristic acoustic impedance ([M·L^-2·T⁻¹]; N·s/m³ or Pa·s/m)

ρ is the density of the medium ([M·L⁻³]; kg/m³), and

c is the longitudinal wave speed or sound speed ([L·T⁻¹]; m/s)

The characteristic impedance of air at room temperature is about 420 Pa s/m. By comparison the sound speed and density of water are much higher, resulting in an impedance of 1.5 MPa s/m, about 3400 times higher. This differences leads to important differences between room acoustics or atmospheric acoustics on the one hand, and and underwater acoustics on the other. 1. ... In physics, density is mass m per unit volume V. For the common case of a homogeneous substance, it is expressed as: where, in SI units: ρ (rho) is the density of the substance, measured in kg·m-3 m is the mass of the substance, measured in kg V is... Longitudinal waves are waves that have vibrations along or parallel to their direction of travel. ... The speed of sound varies depending on the medium through which the sound waves pass. ... Room acoustics describes how sound behaves in an enclosed space. ... Underwater acoustics is the study of the propagation of sound in water and the interaction of the mechanical waves that constitute sound with the water and its boundaries. ...

Specific impedance of acoustic components

The specific acoustic impedance z of an acoustic component (in N·s/m³) is the ratio of sound pressure p to particle velocity v at its connection point: // Sound pressure Sound pressure is the pressure deviation from the local ambient pressure caused by a sound wave. ... Particle velocity is the velocity v of a particle (real or imagined) in a medium as it transmits a wave. ...

where

p is the sound pressure (N/m² or Pa),

v is the particle velocity (m/s), and

I is the sound intensity (W/m²)

// Sound pressure Sound pressure is the pressure deviation from the local ambient pressure caused by a sound wave. ... Particle velocity is the velocity v of a particle (real or imagined) in a medium as it transmits a wave. ... The sound intensity, I, (acoustic intensity) is defined as the sound power Pac per unit area A. The usual context is the noise measurement of sound intensity in the air at a listeners location. ...

Complex impedance

In general, a phase relation exists between the pressure and the particle velocity. The complex impedance is defined as

Z = R + iX

where

R is the resistive part, and

X is the reactive part of the impedance

The resistive part represents the various loss mechanisms an acoustic wave experiences such as random thermal motion. For the case of propagation through a duct, wall vibrations and viscous forces at the air/wall interface (boundary layer) can also have a significant effect, especially at high frequencies for the latter. For resistive effects, energy is removed from the wave and converted into other forms. This energy is said to be 'lost from the system'.

The reactive part represents the ability of air to store the kinetic energy of the wave as potential energy since air is a compressible medium. It does so by compression and rarefaction. The electrical analogy for this is the capacitor's ability to store and dump electric charge, hence storing and releasing energy in the electic field between the capacitor plates. For reactive effects, energy is not lost from the system but converted between kinetic and potential forms.

The phase of the impedance is then given by

Impedance and the input impulse response

Impedance is a frequency-domain parameter. The input impulse response (IIR) is a time-domain parameter and is closely related to the impedance via the Fourier transform. Specifically the IIR is defined as the real part of the inverse Fourier transform of the reflection function

where

is the reflection coefficient

f is the frequency (Hz)

See also

• Electrical impedance
• Acoustic ohm

Electrical impedance, or simply impedance, is a measure of opposition to a sinusoidal alternating electric current. ... The acoustic ohm is a unit of measurement of acoustic impedance, or resistance. ...

External links

• Ohm's law as acoustic equivalent - calculation of acoustic impedance Z, sound pressure, particle velocity, and sound intensity
• Relationships of acoustic quantities associated with a plane progressive acoustic sound wave - pdf