Acoustic impedance

Acoustic impedance is a measure of the resistance a material system presents to the flow of sound resulting from an acoustic pressure applied to the system. It is a characteristic property of the medium in which the wave propagates.

Numerically, acoustic impedance is equal to the ratio of the sound pressure to the volume flow rate associated with particle vibration at a point. An alternative definition is that of specific acoustic impedance, which is the ratio of sound pressure to the velocity of propagation of the wave.

There is a close analogy to electrical impedance, which measures the resistance a system presents to the electrical flow caused by an electrical voltage applied to the system.

The SI unit of acoustic impedance is the pascal second per cubic metre (Pa·s/m3). There is a close analogy with electrical impedance, which measures the opposition that a system presents to the electrical flow resulting from an electrical voltage applied to the system.

Acoustic impedance is typically calculated or measured in the oscillatory regime and is therefore a frequency dependent quantity with amplitude and phase. The amplitude indicates the ratio of the modulus of the oscillatory pressure to the modulus of the oscillatory flow, while the phase indicates how far the fluid flow lags behind or ahead of the pressure motion.

Applications

• Acoustic impedance is a physical quantity particularly suited to describing the response of a musical instrument at different frequencies. It is, in fact, a characteristic of the instrument, independent of the performer who plays it. However, do not think that the quality of an instrument can be uniquely determined by measuring its frequency response. In fact, quality is not an objective parameter and must be judged on a case-by-case basis by human listeners (see the discussion of individual musical instruments). Response, on the other hand, is an objective property of the physical system. One can, of course, discuss how quality and response are related.
• As far as the resistive component is concerned, we can say that if an acoustic system has a “large” specific impedance, it means that a large acoustic pressure is needed to achieve a high fluid velocity. Conversely, if the impedance is small, it means that even a small acoustic pressure is capable of producing a fluid flow with considerable velocity.
• As for reactive components (analogous to electrical capacitance and inductance), the fluid does not dissipate energy, but converts it from kinetic energy to elastic potential energy or vice versa. However, the net effect depends on the frequency, just as in the electrical and mechanical cases, and thus there can be a “filter effect” (attenuation at certain frequencies, but not at others). This effect is well illustrated in the case of resonance (see also harmonic oscillator impedance).
• At resonance, the impedance of an acoustic system takes on a much smaller value than the out-of-resonance value. However, wind instruments can operate at the minimum or maximum of their impedance, depending on the type of coupling between the source of the vibrations and the resonating body. See flute and clarinet as examples of instruments that operate at impedance minima and maxima, respectively.
• Air has its own characteristic impedance, which is temperature-dependent, but has an average value of about 410-415 Pa s/m at room temperature and sea level. The value of this impedance also coincides with the specific impedance of a cylindrical hole, which is therefore independent of the design details of the hole itself.
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