We measure the power spectrum of density fluctuations emerged in a freely expanding quasi-two-dimensional (2D) degenerate Bose gas and investigate the scaling behavior of the spectrum for the expansion time. The power spectrum shows an oscillatory shape for long expansion times, where the spectral peak positions are observed to be shifted to lower spatial frequencies than the theoretical prediction for a non-interacting expansion case. We find the spectral peak positions in good agreement with

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... he recent numerical simulation presented by Mazets [Phys. Rev. A 86, 055603 (2012)], where the atom-atom interactions are taken into account. We present a mean-field description of the interaction effect in the expansion dynamics and quantitatively account for the observed spectral peak shifts. The spectral shift is intrinsic to the free expansion of a quasi-2D Bose gas due to finite axial confinement. Finally, we investigate the defocussing effect in the power spectrum measurement.