A few days ago, I sent my rough draft "Evanescent Liquid-Sound-Pressure Waves Near an Underwater Wineglass" to seven List Members. In the meantime, I have studied those sounds with a microphone and an oscilloscope. All three frequency values given at the beginning of the mentioned draft turned out to be too low by one octave. True frequencies: ~1040 Hz (empty, case A), ~620 Hz (full, case B), and ~420 Hz (submerged, case C). Also, I found a way to predict those frequencies under the assumption of a z-independent oscillation mode with nodes at phi = pi/4, 3pi/4, 5pi/4, and 7pi/4. I equalled the maximal potential energy of the system to the work required to squeeze the glass into its initial elliptical shape, and to the maximal kinetic energy of the glass and (in cases B and C) of the water. The predicted frequencies were lower, by about one octave, than the measured wineglass frequencies. In the case of pieces of metal tubing, however, experiment and theory agreed.
Such evanescent waves occur, e.g., in the cochlea. They are predicted to exist also in strictly incompressible liquids. They are standing waves. Liquid particles oscillate on short straight-line segments. The liquid particle is accelerated, then decelerated and forced to return by the local sound-pressure gradient. No textbook description of these waves has been mentioned to me so far. Soon I will start to think about submitting an abstract on these wineglass calculations to the CAA meeting in Victoria (October 2010).
Dr. phil. nat.,
r. PSI and ETH Zurich,
Phone: 0041 56 441 77 72.
Mobile: 0041 79 754 30 32.
E-mail: reinifrosch@xxxxxxxxxx .