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This study is concerned with the spatial structures of n-dimensional random waves in homogenexus media.The joint probability distribution of apparent amplitude,wave number and phase is derived.Based on this joint distribution, we define the apparent wave number spectrum and derive that the upper limit of the equilibrium range exponent of this spectrum is-(n+2).In case of 2-dimension, the upper limit of the equilibrium range exponent of the apparent wave number spectrum is consistent with the equilibrium range exponent of the Fourier wave number spectrum derived from dynamics.