Estimation of number of modes in periodic graphs
M. S. Dorofeev, Andrey V. Shanin · Waves in Random and Complex Media · 2009
The problem of acoustic wave propagation in a one-periodic system of thin pipes is studied. A dispersion equation linking the time frequency ω with the propagation constant (quasimomentum) γ is derived. A particular question is studied, namely how many different values of γ can obey the dispersion equation for a fixed ω. A simple estimation of this amount is obtained in terms of the properties of the graph representing a single period of the system.