Easy method to establish the dispersion relation of capillary waves on water jets

Abstract

A simple, intuitive, and low-cost setup for generating and measuring capillary waves is presented enabling a precise determination of the dispersion relation for a cylindrical water jet. By setting the phase velocity and measuring the wavelength of capillary waves directly, this method provides an intuitive way for students to understand the dispersion relation of a cylindrical water jet. The setup produced measurements of wavelength versus phase velocity over a broader range of values than earlier work. The resulting data are generally consistent with earlier results but show an error of up to 15% at both the higher and lower end of the measured range of wavelengths compared to the theoretical dispersion relation of cylindrical water jets. For the shorter wavelengths, the deviation is in the opposite direction from that of earlier work.