Dear colleagues,
The low-frequency standing surface waves observable in water-filled bathtubs and in similar troughs are gravity-driven, whereas the standing evanescent liquid sound-pressure waves in water-filled drinking glasses tapped with spoons (and possibly in the human cochlea during spontaneous oto-acoustic emissions) are spring-driven. Nevertheless the two wave categories have similar streamline patterns and similar patterns of constant-pressure-amplitude lines. Therefore the low-frequency waves can be used in classroom demonstrations as introduction into the subject of evanescent liquid sound-pressure waves.
The low-frequency waves are treated in a recent paper by S. J. Sinick and J. J. Lynch, "Surface Gravity Waves: Resonance in a Fish Tank", The Physics Teacher 48 (2010) 330-332. Reference 3 of that paper is the book "Hydrodynamics" by Sir Horace Lamb, 6th ed. (1932). In Chapter IX of that textbook, "Surface Waves", standing surface gravity waves in a horizontal sheet of water are discussed in detail. Eq. (11) [page 365] gives the liquid-particle displacements versus time and place for arbitrary water-sheet thickness, and in a diagram on page 366, the streamlines are shown for sheet thickness much greater than the wavelength. In the text below that diagram, it is mentioned that these waves occur in troughs if their vertical walls coincide with antinodes (where the liquid particles oscillate vertically).
Reinhart.
Reinhart Frosch,
Dr. phil. nat.,
CH-5200 Brugg.
reinifrosch@xxxxxxxxxx .