Читать книгу Engineering Acoustics - Malcolm J. Crocker - Страница 121

Near to a source, we call the sound field, the near acoustic field. Far from the source, we call the field the far acoustic field. The extent of the near field depends on:

1 The type of source: (monopole, dipole, size of machine, type of machine, etc.)

2 Frequency of the sound.

In the near field of a source, the sound pressure and particle velocity tend to be very nearly out of phase (≈90°).

In the far field, the sound pressure and particle velocity are very nearly in phase. Note, far from any source, the sound wave fronts flatten out in curvature, and the waves appear to an observer to be like plane waves. In‐plane progressive waves, the sound pressure and particle velocity are in phase (provided there are no reflected waves). Thus far from a source (or in a plane progressive wave) p/u = ρc. Note ρc is a real number, so the sound pressure p and particle velocity u must be in phase.

Figure 3.17 shows the example of a finite monopole source with a normal simple harmonic velocity amplitude U. On the surface of the monopole, the surface velocity is equal to the particle velocity. The particle velocity decreases in inverse proportion to the distance from the source center O.

Figure 3.17 Example of monopole. On the monopole surface, velocity of surface U = particle velocity in the fluid.

It is common to make the assumption that kr = 2πf r/c = 10 is the boundary between the near and far fields. Note this is only one criterion and that there is no sharp boundary, but only a gradual transition. First we should also think of the type and the dimensions of the source and assume, say that r ≫ d, where d is a source dimension. We might say that r > 10d should also be applied as a secondary criterion to determine when we are in the far field.