Instantaneous and time-averaged energy transfer in acoustic fields

The fundamentals of energy transfer in an acoustic field are addressed and it is shown that describing the flux of energy in an acoustic field with the active intensity alone is inaccurate. A single active intensity vector describes only the time-average energy flux at a point in space, but not where the energy came from nor where it is going. Consequently, the instantaneous intensity must be used to properly describe energy flux as a time-dependent process. The phenomenon of the acoustic vortex is examined and, from the perspective of active intensity, it is seen to represent a resultant wave rotating around a zero pressure line or point at which the pressure phase is discontinuous. It is shown that this resultant wave travels with a phase speed cp, which is generally different than the plane-wave phase speed c. The instantaneous intensity, however, shows that energy is flowing through the vortex and not with the resultant waves. Although the complex intensity vector is normally separated into the active and reactive components (i.e., rotational and solenoidal parts), the active intensity can be further represented by two parts, one with zero and another with nonzero curl, which permits the representation of the coupling between sources or parts of a source. In general, this article emphasizes the physical meaning and interpretation of energy related quantities.