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Second Sound in Square and Cubical Cavities

1964; American Institute of Physics; Volume: 136; Issue: 4A Linguagem: Inglês

10.1103/physrev.136.a918

1536-6065

P. J. Bendt,

Experimental and Theoretical Physics Studies

The response of closed square and cubical cavities to linear standing waves of second sound in helium ii has been studied. In a square cavity, when the number of half-wavelengths $n$ along one side is even, a linear wave in the $x$ direction couples loosely with the $y$ direction, producing standing waves in both directions at two resonant frequencies, in a narrow doublet. The theory of the coupled waves is analogous to that for coupled LC electric circuits. When $n$ is odd, a linear wave does not couple with the perpendicular directions. However, owing to quadratic terms in the thermohydrodynamic equations, a small-amplitude wave at twice the frequency of the standing wave is generated, and this wave is present along both the $x$ and $y$ axes. A theory of these phenomena is presented, along with frequency, amplitude, phase, and $Q$ measurements. The results are similar in cubical cavities, but the number of available coupled-wave modes is reduced by cancellation of waves, due to the symmetry of the cavity.