Evanescent waves in the bathtub.

Dear colleagues,

Please permit me to post one more mini-tutorial. As mentioned before, evanescent (standing) liquid sound-pressure waves are the main cause of the frequency reduction observed if a drinking glass tapped with a spoon is filled with liquid. According to one model, these waves occur also during the generation of SOAEs (spontaneous oto-acoustic emissions) in the cochlea. Standing waves which are similar but have frequencies of only about one hertz can be observed in a filled bathtub. If one uses the flat hands to push the water surface down near one of the long walls, then a one-hertz oscillation can be generated. The water particles at the center of the surface oscillate horizontally. The wavelength lambda equals twice the width of the surface, i.e., lambda = 1.1 m approximately. Wave number: k = 2pi / lambda = 5.7 m^-1. If one treats this standing wave as the superposition of two travelling liquid surface waves in opposite directions, one obtains a predicted frequency of
f = [1/(2pi)] * sqrt[g*k*tanh(k*H)] = 1.15 Hz;
H = 0.3 m is the water depth; g = 9.8 m/s^2 is the free-fall acceleration.

Reinhart.

Reinhart Frosch,
Dr. phil. nat.,
CH-5200 Brugg.
reinifrosch@xxxxxxxxxx .