Acoustic impedance
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| Sound measurements |
|---|
| Sound pressure p |
| Sound pressure level (SPL) |
| Particle velocity v |
| Particle velocity level (SVL) |
| (Sound velocity level) |
| Particle displacement ξ |
| Sound intensity I |
| Sound intensity level (SIL) |
| Sound power Pac |
| Sound power level (SWL) |
| Sound energy density E |
| Sound energy flux q |
| Acoustic impedance Z |
| Speed of sound c |
The acoustic impedance Z (or sound impedance) is the ratio of sound pressure p to particle velocity v in a medium or acoustic component. Z can be either measured in its constituent units (pressure per velocity) or in rayls.
Distinction has to be made between:
- the characteristic acoustic impedance <math>Z_0</math> of a medium, usually air (compare with characteristic impedance in transmission lines).
- the impedance <math>Z</math> of an acoustic component, like a wave conductor, a resonance chamber, a muffler or an organ pipe.
Contents |
[edit] Characteristic impedance
The characteristic impedance of a medium (usually air, but also for instance exhaust gases in a muffler) is the ratio of sound pressure p to particle velocity v in open field (i.e. in a condition of no reflecting waves). This impedance is a material constant and equals the product of the density of air ρ (rho) and the speed of sound c:
- <math>
Z_0 = \rho \cdot c </math>
ρ (rho) = density of air in kg/m3
c = speed of sound (acoustic wave velocity) in m/s
Note: <math>Z_0</math> is expressed in Pa·s/m. Before the pascal was introduced by the SI, impedance was expressed in N·s/m3.
The characteristic acoustic impedance of air at one atmosphere pressure <math>Z_0</math> equals:
- 410 Pa·s/m at a temperature of 25 °C (77 °F)
- 413 Pa·s/m at 20 °C (68 °F).
°C = degree Celsius and °F = degree Fahrenheit.
Table - Acoustic impedance <math>Z_0</math>, Speed of sound in air c, density of air ρ vs. temperature °C at 1 atm pressure
| Impact of temperature | |||
|---|---|---|---|
| °C | Z in Pa·s/m | c in m/s | ρ in kg/m³ |
| − 10 | 436.5 | 325.4 | 1.341 |
| − 5 | 432.4 | 328.5 | 1.316 |
| 0 | 428.3 | 331.5 | 1.293 |
| + 5 | 424.5 | 334.5 | 1.269 |
| + 10 | 420.7 | 337.5 | 1.247 |
| + 15 | 417.0 | 340.5 | 1.225 |
| + 20 | 413.5 | 343.4 | 1.204 |
| + 25 | 410.0 | 346.3 | 1.184 |
| + 30 | 406.6 | 349.2 | 1.164 |
[edit] Impedance of acoustic components
The acoustic impedance Z of an acoustic component (in Pa·s/m) is the ratio of sound pressure p to particle velocity v at a transition with a previous component:
- <math>
Z = \frac{p}{v} = \frac{I}{v^2} = \frac{p^2}{I} </math>
p = sound pressure in N/m2 = Pa = pascal
v = particle velocity in m/s
I = sound intensity in W/m2
