  A system of two-dimensional, two coupled Faraday interfacial waves is
experimentally observed at the two interfaces of the three layers of fluids
(air, pure ethanol and silicon oil) in a sealed Hele-Shaw cell with periodic
vertical vibration. The upper and lower Faraday waves coexist: the upper
vibrates vertically, but the crests of the lower one oscillate horizontally
with unchanged wave height and a frequency equal to the half of the forcing one
of the vertically vibrating basin, while the troughs of the lower one always
stay in the same place (relative to the basin). Besides, they are strongly
coupled: the wave height of the lower Faraday wave is either a linear function
(in the case of a fixed forcing frequency) or a parabolic function (in the case
of a fixed acceleration amplitude) of that of the upper, with the same wave
length. In addition, the upper Faraday wave temporarily loses its smoothness at
around $t=T/4$ and $t=3T/4$, where $T$ denotes the wave period, and thus has
fundamental difference from the traditional one. To the best of our knowledge,
this system of the two coupled Faraday waves has never been reported.
