Acoustic response of a rectangular waveguide with a strong transverse temperature gradient

An acoustic wave equation was developed for a perfect gas with spatially-variable temperature. The strong-gradient wave equation was used to analyze the response of a rectangular wave guide containing a thermally-stratified gas. It was assumed that the temperature gradient is constant, representing one-dimensional heat transfer with a constant coefficient of conductivity. The analysis of the waveguide shows that the resonant frequencies of the waveguide are shifted away from the values that would be expected from the average temperature of the waveguide. For small gradients, the frequency shift is proportional to the square of the gradient. The factor of proportionality is a quadratic function of the natural frequency of the waveguide with uniform temperature. An experiment is designed to verify the essential features of the strong-gradient theory.