The propagation speed of small-amplitude surface waves in a region of uniform depth is given by

\[c^{2}=\left(\frac{2 \pi \sigma}{\lambda ho}+\frac{g \lambda}{2 \pi}\right) \tanh \frac{2 \pi h}{\lambda}\]

where \(h\) is depth of the undisturbed liquid and \(\lambda\) is wavelength. Explore the variation in wave propagation speed for a free-surface flow of water. Find the operating depth to minimize the speed of capillary waves (waves with small wavelength, also called ripples). First assume wavelength is much smaller than water depth. Then explore the effect of depth. What depth do you recommend for a water table used to visualize compressible flow wave phenomena? What is the effect of reducing surface tension by adding a surfactant?