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In the study of the surface instability of a vertically oscillating granular layer, we obtained experimentally thephase diagram for the surface states of the layer in the driving frequency-acceleration plane, and measured thedispersion relation for the surface waves in a granular layer in comparison to that in viscous fluids. Our experiments show that the onset dimensionless acceleration increases with the driving frequency, and the wavelengthof the surface waves increases with the depth of granular layer. These experimental results are in agreement withour theoretical model qualitatively.