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We have calculated the first and second sound modes of a dilute interacting Bose gas in a spherical trap for temperatures (0.6<T/Tc<1.2) and for systems with 10⁴ to 10⁸ particles. The second sound modes (which exist only below Tc) generally have a stronger temperature dependence than the first sound modes. The puzzling temperature variations of the sound modes near Tc recently observed at JILA in systems with 10³ particles match surprisingly well with those of the first and second sound modes of much larger systems.
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Shenoy et al. (1998) studied this question.