= Solution
\b[Sound propagation.] In the 1997 experiment, a focused laser beam abruptly modified the trapping potential of a dilute condensate, producing a local excitation. A rapid sequence of nondestructive <phase-contrast imaging> measurements followed the resulting <density> motion. Measuring propagation <speed> at different densities tested the sound-like collective excitation spectrum, rather than individual free-particle flight.<Propagation of Sound in a Bose-Einstein Condensate by M. R. Andrews and others>[1997, primary abstract and author publication record; Physical Review Letters 79, 549–552, with 1998 erratum]{ref} For a weakly interacting uniform condensate, the <Bogoliubov spectrum> is
$$
\epsilon(p)=\sqrt{\frac{p^2}{2m}\left(\frac{p^2}{2m}+2gn\right)},
\qquad c_s=\lim_{p\to0}\frac{\epsilon(p)}p=\sqrt{\frac{gn}{m}}.
$$
<Density> dependence and trapped-geometry averaging matter when comparing a measured pulse <speed> with this local uniform formula. A strictly <ideal gas> would have no nonzero interaction-supported sound <speed>.
\b[Moving-obstacle dissipation.] In the 1999 experiment, a blue-detuned focused beam repelled atoms and acted as an obstacle swept through a sodium condensate. Heating was inferred from the <condensate fraction> after stirring and re-equilibration. The heating rose markedly near $1.6\,\mathrm{mm\,s^{-1}}$, below the quoted peak sound <speed> $6.2\,\mathrm{mm\,s^{-1}}$.<Evidence for a Critical Velocity in a Bose-Einstein Condensed Gas by C. Raman and others>[pages 2502–2504, obstacle method, heating onset and comparison with sound]{ref} Landau's criterion $v_L=\inf_p\epsilon(p)/p$ motivates a dissipation threshold, but <density> variation, flow acceleration around the obstacle and <vortex> nucleation make the observed threshold different from simply substituting the peak sound <speed>. \b[Together these experiments probe a collective excitation spectrum and the onset of dissipative flow; condensation alone is not a complete demonstration of <superfluidity>.]
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