Question1

A square membrane with sides of length L, uniform mass density per unit area σ, and uniform surface tension S is free on the side at x = L but set on other three sides.

(a) Establish the wave functions and the general expression for the angular frequency of the normal modes. What is an angular frequency of the (lowest lying) fundamental mode?

(b) Draw the nodal patterns for the five normal modes with the lowest frequencies.

Question2

Two strings, of tension T and mass densities μ1 and μ2, are connected together. Think about a travelling wave incident on the boundary. Illustrate that the energy flux of the reflected wave plus the energy flux of the transmitted wave equals the energy flux of the incident wave. The energy flux of a wave is given by the energy density times the wave speed.