# Acoustic impedance

Sound quantities

The characteristic acoustic impedance , also known as acoustic field impedance or specific acoustic impedance , is one of the three definitions of impedance used in acoustics , together with acoustic flow impedance and mechanical impedance . ${\ displaystyle Z_ {F}}$

The characteristic acoustic impedance is the specific impedance, which is called the wave resistance of the medium . Acoustic impedance or acoustic impedance are outdated terms for the characteristic acoustic impedance, a physically less meaningful label is sound hardness .

## description

The characteristic sound impedance is a physical quantity and is defined as the ratio of sound pressure  p to sound velocity  v :

${\ displaystyle {\ underline {Z_ {F}}} = {\ frac {\ {\ underline {p}} \} {\ {\ underline {v}} \}}}$

Sound pressure and sound velocity and thus also the acoustic field impedance are generally described here as complex quantities that each depend on the frequency .

The derived SI unit of the characteristic sound impedance is Ns / m 3 (outdated: Rayl ).

In the far field , pressure and velocity are in phase , which is why the characteristic sound impedance is calculated as a real value :

${\ displaystyle Z_ {F} = {\ frac {p} {v}} = {\ frac {I} {v ^ {2}}} = {\ frac {p ^ {2}} {I}} = \ rho \ cdot c}$

With

• the sound intensity ${\ displaystyle I}$
• the speed of sound ${\ displaystyle c}$
• the density .${\ displaystyle \ rho}$

The above equation shows that the product of density and speed of sound is equal to the characteristic sound impedance and is therefore constant in space and time in a homogeneous , invariant sound field . This relationship is also called " Ohm's law as acoustic equivalence" .

The constant of proportionality between sound pressure and speed is also known as wave resistance. The word "resistance" is supposed to signal the analogy to the electrical resistance R  =  U  /  I , since the electrical voltage is related to the force in a similar way to the sound pressure and the electrical current is related to a particle flow similar to the speed .

If sound waves move from one medium to another (e.g. from air in water), they are reflected more strongly at the interface (in this case the water surface), the more different the characteristic sound impedances of the two media are. The sound reflection factor is the ratio of the sound pressure p r of the wave reflected at the interface to the sound pressure p e of the incident wave; it is also the ratio of the difference between the two characteristic sound impedances to their sum in the case of perpendicular sound incidence: ${\ displaystyle r}$

${\ displaystyle r = {\ frac {p_ {r}} {p_ {e}}} = {\ frac {Z_ {2} -Z_ {1}} {Z_ {2} + Z_ {1}}}}$

## Pressure and temperature dependence for gases

In contrast to liquids and solids, the acoustic impedance of gases depends significantly on the state variables pressure and temperature : for ideal gases it is proportional to and to : ${\ displaystyle p}$${\ displaystyle {\ frac {1} {\ sqrt {T}}}}$

${\ displaystyle Z_ {F} = p \, {\ sqrt {\ kappa \, {\ frac {M} {R \, T}}}}}}$

with the material constants :

For a pressure of 100 k Pa and a temperature of 20 ° C that is, a current average rate of change of about 1% / kPa and -0.17% / K .

Characteristic acoustic impedance of air as a function of temperature at 101,325 Pa
Temperature in ° C
${\ displaystyle \ vartheta}$
Characteristic impedance in Ns / m³
${\ displaystyle Z _ {\ text {F}}}$
Temperature in ° C
${\ displaystyle \ vartheta}$
Characteristic impedance in Ns / m³
${\ displaystyle Z _ {\ text {F}}}$
+40 400.2 +5 424.5
+35 403.4 0 428.3
+30 406.7 −5 432.3
+25 410.0 −10 436.4
+20 413.6 −15 440.6
+15 417.1 −20 444.9
+10 420.8 −25 449.4

## Material dependency

Characteristic acoustic impedance of gases (at 101,325 Pa and 0 ° C)
gas ρ
[kg / m 3 ]
c
[m / s]
Z F
[Ns / m 3 ]
argon 1.78 308 550
helium 0.1786 972 173.7
krypton 3.74 212 795
air 1.2920 331.5 428.3
neon 0.90 433 390
Sulfur hexafluoride 6.63 144 955
nitrogen 1.245 337 421
hydrogen 0.08994 1256 113
xenon 5.8982 170 995
Ideal gas ${\ displaystyle {\ frac {p \, M} {R \, T}}}$ ${\ displaystyle {\ sqrt {\, \ kappa \, {\ frac {R \, T} {M}}}}}$ ${\ displaystyle p \, {\ sqrt {\, \ kappa \, {\ frac {M} {R \, T}}}}}$
Characteristic acoustic impedance of liquids
liquid θ
[° C]
ρ
[10 3  kg / m 3 ]
c
[10 3  m / s]
Z F
[10 6  Ns / m 3 ]
benzene 20th 0.88 1.326 1.167
bromine 20th 3.12 0.149 0.465
Ethanol 20th 0.7893 1.168 0.922
Galinstan 20th 6.44 2.95 19.0
Pentane 20th 0.621 1.01 0.627
mercury 20th 13,546 1.407 19.059
water 0 0.999.84 1.403 1.403
10 0.999.70 1,448 1,448
20th 0,998.20 1.483 1,480
30th 0,995.64 1.509 1.502
40 0.992.21 1.529 1.517
50 0.988.03 1.543 1.525
60 0.983.19 1.551 1.525
70 0.977.76 1.555 1.520
80 0.971.79 1.555 1.511
90 0.965.30 1.551 1.497
100 0.958.35 1.543 1.479
liquid ${\ displaystyle \ vartheta}$ ${\ displaystyle \ rho}$ ${\ displaystyle {\ sqrt {\, {\ frac {K} {\ rho}}}}}$ ${\ displaystyle {\ sqrt {\, \ rho \, K}}}$
Longitudinal acoustic impedance of solids
material ρ
[10 3  kg / m 3 ]
c
[10 3  m / s]
Z F
[10 6  Ns / m 3 ]
aluminum 2.70 6.42 16.9 *
Lead zirconate titanate 7.8 3.85 30 *
diamond 3.52 18.35 64.6 *
Ice (0 ° C) 0.918 3.25 2.98
iron 7,874 5.91 45.6 *
copper 8.93 5.01 44.6
lithium 0.535 6th 3.2
magnesium 1.73 5.8 10
Brass (30% tin) 8.64 4.7 40.6
Natural rubber 0.95 1.55 1.4 *
Polystyrene 1.06 approx. 2.2 2.3 *
steel approx 7.85 about 6 approx 45
titanium 4.50 4.14 18.6
tungsten 19.25 5.22 104.2 *
Solid (longitudinal) ${\ displaystyle \ rho}$ ${\ displaystyle {\ sqrt {\, {\ frac {K + {\ frac {4} {3}} G} {\ rho}}}}}$ ${\ displaystyle {\ sqrt {\, \ rho \ left (K + {\ frac {4} {3}} G \ right)}}}$
Solid (transversal) ${\ displaystyle {\ sqrt {\, {\ frac {G} {\ rho}}}}}$ ${\ displaystyle {\ sqrt {\, \ rho \, G}}}$

Material constants :

• * Textbook of physics: Vol. 1: Mechanics, acoustics, thermodynamics. Ernst Grimsehl, Walter Schallreuter. P. 256.
• Further values ​​for solids can be found under.