Pure tone modes for a 5:3 elliptic drum

TL;DR

This paper explores the standing modes of a 5:3 elliptic drum using Mathieu functions, employing Newton's method and the Squire-Trapp formula to compute and tabulate low-frequency modes.

Contribution

It introduces a novel computational approach for determining elliptic drum modes using Mathieu functions and provides detailed tabulations of low-frequency solutions.

Findings

Computed several standing modes for the elliptic drum

Developed a method using Newton's method and Mathieu functions

Provided tabulated values for low-frequency modes

Abstract

The paper exhibits several standing modes of a 5:3 elliptic drum computed using Mathieu functions. To match the boundary conditions, I used Newton's method on the appropriate modified Mathieu equation using the Squire-Trapp formula for computing derivatives. I tabulate the requisite values of the parameter $q$ for these low-frequency modes.