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Surface waves of a homogeneous liquid and internal waves of a stratified liquid in basins of variable depth are considered. Inequalities involving the frequencies of oscillation are obtained when a container with one size or geometry is compared with another with a different size or geometry, when waves with one wavelength are compared with waves with another wavelength, or when one stratification is compared with another. Since exact solutions for gravity waves in basins of variable depth are so rare, one hopes the comparison theorems presented herein will be useful.

Comparison theorems for gravity waves in basins of variable depth