Phase Shifts in Point Source Waves: Exploring the Why & How

[The_Lobster]

My text says that as we approach a point source (of e.g. sound) from a distance, the phase angle between pressure and particle velocity will gradually shift from zero (in the far field/plane waves) to 90˚ (in the near field/spherical waves).

I can't find any intuitive explanation of why this is the case? Why do spherical waves have the phase shift, and plane waves don't, and vice versa?

Secondly, the text says that the particle velocity will increase with this increasing phase shift as we get closer to the source; but I have a feeling this might be explained by the above?

Thanks in advance! :)

 

[gtoguy97]

The answer to your first question is that the phase angle shift between pressure and particle velocity has to do with the nature of the wave as it propagates through space. In the far field, or plane wave region, the wave fronts are flat and the individual wave components (pressure and particle velocity) move at the same speed – so they maintain the same phase relationship. In the near field, or spherical wave region, the wave fronts are curved and the individual wave components move at different speeds, resulting in a phase shift between the two. The answer to your second question is that the increasing particle velocity is a result of the increasing phase shift. As the wave moves into the near field, its wavelength shortens and the particle velocity increases. This is due to the fact that the particle velocity is determined by the rate of change of the wave's pressure, which is higher in the near field than in the far field.