Natural Science Forum / Physics / Acoustics / May 2005

You have to be more specific about what  you are asking.  Are you asking why
pressure and velocity are not always in-phase?  Or are you asking why phase
changes with respect to some other variable (e.g., frequency, position,
etc.)?  Answering a "why" question is sometimes difficult.  In general,
physics dictates that an object vibrating in open space at low frequency
(i.e., small ka) has a surface impedance (p/v)  that is approximately purely
imaginary (mass-like, since p and v are 90 degrees out-of-phase) and
non-local.  At very high frequency, the impedance is approximately real
(damper-like, since p and v are in-phase) and local.  In between, there
clearly has to be a transition.  Also, with respect to distance, regardless
of the nature of surface impedance, p and v are in-phase in the far-field.
These observations are direct consequences of the Helmholtz integral
equation.