In introductory physics courses, simple arguments based on traveling waves on a string are used to relate the frequency of standing waves to boundary conditions, e.g., the fixed ends of the string. Here, we extend that approach to two-dimensional waves such as the oscillations of a rectangular membrane with edges fixed at the boundary. This results in a graphical method that uses only simple geometry and is suitable for explaining two-dimensional standing-wave oscillations to non-science majors, e.g., in a physics of sound and music class.
Romano, Joseph D., and Richard H. Price. "A simple graphical method for calculating the standing wave frequencies on a rectangular membrane." American Journal of Physics 88, no. 8 (2020): 605-611. https://doi.org/10.1119/10.0001299
American Journal of Physics