  This study develops a ray technique for determining the resonance frequencies
of triangular membranes. The technique is demonstrated for homogenous
rectangular and triangular membranes with fixed boundaries. Where possible, the
results are compared with exact calculations. The membrane resonances are
calculated using an equivalent string whose length is proportional to the
reciprocal of the length of closed paths starting from an arbitrary point
within the membrane. Closed paths are ray paths which arrive back at the
starting point going in the same direction.
