Third-sound propagation in thick films of superfluid He-4

Atkins' (1959) basic theory of third sound in thick films of superfluid He-4 is extended here to include a heat source for exciting third sound. A one-dimensional model obeying periodic boundary conditions is developed which can represent a variety of experimentally important configurations. General solutions for the model equations are found which give a complete description of third-sound waves in terms of displacement of the film surface, superfluid velocity, and temperature change as functions of space and time. Algebraic expressions for quantities that occur in general formulas are found for special excitation signals. The structure of third sound is calculated for the first time and the results are found to be inconsistent with previous findings. A direct method for accurately measuring the vaporization coefficient is also presented.