Characterizing Seiche Formed in a Backyard Pool

A barotropic seiche is effectively a standing wave that forms in the surface of an enclosed basin such as a lake. Artificial seiche can be created by rhythmically driving the water surface of a back yard pool. In three experiments, we excite different seiche modes in the surface of a pool and analyze their characteristics. An ultrasonic sensor positioned near the outer edge of the pool recorded the location of the water surface as a function time. The surface height time series is Fourier analyzed to determine the frequency of the observed modes. In cylindrical systems, the spatial solution to wave equation is provided by Bessel functions of the first kind. The admitted modes are those that meet the boundary condition that the gradient of the Bessel function is zero at the center and outer edge of the pool. A dispersion relationship constructed from the observed angular frequencies and wave numbers of the corresponding admitted modes shows excellent agreement with the general water wave dispersion relationship. The experiment provides students with experience applying Fourier analysis to a relatively straight forward data set, an appreciation for how the dispersion relationship relates the wave characteristics to the physical properties of the system and a tangible analog for visualizing quantum mechanical systems.