This is an animation of the analytic solution, for the acoustic field of a pulsating tube, described by Blackstock "Fundamentals of Physical Acoustics" p. 409.
What I find interesting here is the following. You have an approximation of the impedance Z in the near field, equation (C-20), then you can use it to approximate the value of pressure in the surrface of the tube, as p=Zu, and it is expected this approximation will improve as the tube radius, a, decreases. This animation shows that the convergence rate is really slow, mainly because of the phase shift, for a tube with a radius a million times smaller than the wavelegth, the relative error is still in the order of 10%.
Authors: Roberto Velasco Segura and Pablo L. Rendón
Grupo de Acústica y Vibraciones, Centro de Ciencias Aplicadas y Desarrollo Tecnológico (CCADET), Universidad Nacional Autónoma de México (UNAM).