Читать книгу Vibroacoustic Simulation - Alexander Peiffer - Страница 67

The acoustic impedance z is according to Equation (2.38)

(2.76)

In contrast to the plane wave, the specific acoustic impedance is not real. It contains a resistive and a reactive part. When the resistive part is dominant the pressure is in phase with the velocity. When the reactive part dominates, the velocity is out of phase to the pressure. The out of phase component does not generate any power in the sound field as it was the case for moving a mass or driving a spring. The motion is partly introduced into the local kinetic energy, and this part can be recovered as it is the case for an oscillating mass. For the acoustic field of a spherical source the reactive field represents the near-field fluid volume that is carried by the sphere motion but not emitting a wave.

Figure 2.6 Reactance and resistance of specific acoustic impedance of a pulsating sphere. Source: Alexander Peiffer.

There are two limit cases in Equation (2.76):

1 kr≪1; the wave length λ is much larger than distance r.

2 kr≫1; the wave length λ is much smaller than distance r.

Introducing the above approximations into Equation (2.76) gives a fully reactive impedance for (i)

(2.77)

and a resistive part equal to plane waves for (ii)

(2.78)