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We present heuristic arguments suggesting that if EM waves with wavelengthssomewhat larger than the Schwarzschild radius of a black hole were fullyabsorbed by it, the second law of thermodynamics would be violated, under theBekenstein interpretation of the area of a black hole as a measure of itsentropy. Thus, entropy considerations make the well known fact that largewavelengths are only marginally absorbed by black holes, a natural consequenceof thermodynamics. We also study numerically the ingoing radial propagation ofa scalar field wave in a Schwarzschild metric, relaxing the standard assumptionwhich leads to the eikonal equation, that the wave has zero spatial extent. Wefind that if these waves have wavelengths larger that the Schwarzschild radius,they are very substantially reflected, fully to numerical accuracy.Interestingly, this critical wavelength approximately coincides with the onederived from entropy considerations of the EM field, and is consistent withwell known limit results of scattering in the Schwarzschild metric. Thepropagation speed is also calculated and seen to differ from the value $c$, forwavelengths larger than $R_{s}$, in the vicinity of $R_{s}$. As in allclassical wave phenomena, whenever the wavelength is larger or comparable tothe physical size of elements in the system, in this case changes in themetric, the zero extent 'particle' description fails, and the wave naturebecomes apparent.Comment: 14 Pages, 4 figures. Accepted for publication in the Journal Entrop

The Connection Between Entropy and the Absorption Spectra of Schwarzschild Black Holes for Light and Massless Scalar Fields