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Evanescent waves in bathtubs (2).
The liquid-particle motion in the 1.15-hertz oscillation described yesterday differs appreciably from one point in the bath water to the other. In the studied case, the waterline at the two long walls oscillates up and down, staying horizontal. If the amplitude of that oscillation is assumed to amount to 2 cm, then for the assumed dimensions (surface width 55 cm, water height 30 cm) the water particles at the center of the surface oscillate horizontally (in a direction perpendicular to the long walls) with an amplitude of about 2.13 cm. The water particles at the center of the bottom oscillate in the same direction with an amplitude of only about 0.75 cm, and those at the bottom of the long walls of the assumed cubic bathtub do not oscillate at all. So the designation of that standing surface wave as an evanescent wave is justifiable. Is this simple bathtub wave described in textbooks? If yes, then the step to the evanescent waves relevant to acoustics and (possibly) to cochlear mechanics would be small of course.
Dr. phil. nat.,