Acoustic impedance

Sound quantities

Sound deflection ${\displaystyle \xi }$ Sound pressure ${\displaystyle p}$ Sound pressure level ${\displaystyle L_{p}}$ Sound energy density ${\displaystyle E}$ Sound energy ${\displaystyle W}$ Sound flow ${\displaystyle q}$ Speed ​​of sound ${\displaystyle c_{\text{S}}}$ Acoustic impedance ${\displaystyle Z}$ Sound intensity ${\displaystyle I}$ Sound power ${\displaystyle P_{\text{ak}}}$ Speed ​​of sound ${\displaystyle v}$ Fast sound amplitude ${\displaystyle v}$ Sound radiation pressure

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 Acoustic impedance or acoustic impedance are outdated terms for the characteristic acoustic impedance, a physically less meaningful label is sound hardness .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The derived SI unit of the characteristic sound impedance is Ns / m ³ (outdated: Rayl ).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 :

• Adiabatic exponent  κ
• molar mass  M
• Gas constant  R .

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	11.34	1.26	14.3 *
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 :

• ρ : density
• K : compression modulus
• G : shear modulus

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

See also

• List of audio terms

Web links

• Ohm's law as acoustic equivalence - conversion of sound impedance, sound pressure, sound velocity and sound intensity
• Correlation of the acoustic quantities in plane progressive sound waves - pdf (109 kB)
• Comparative representation of sound field quantities and sound energy quantities - pdf (37 kB)

Individual evidence

1. ↑ ^{a b} http://www.rfcafe.com/references/general/velocity-sound-media.htm
2. ↑ Speed ​​of Sound of the elements (engl.)
3. ↑ Archived copy ( memento of the original from January 24, 2016 in the Internet Archive ) Info: The archive link was inserted automatically and has not yet been checked. Please check the original and archive link according to the instructions and then remove this notice.