When a closed vessel containing two stably stratified, immiscible liquids is oscillated in the horizontal direction, the flat interface between the two liquids is known to undergo a symmetry breaking bifurcation to two-dimensional (2-D) 'frozen wave' driven by interfacial shear, similar to the Kelvin-Helmholtz instability. In this thesis we present an experimental study on the dynamics of this interfacial wave as a function of the vibrational Froude number (W, square root of the ratio of vibrational to gravitational forces). The onset of the 'frozen wave' is followed by a nonlinear growth of the wave to large amplitudes, which precedes a secondary instability to three-dimensional (3-D) waves.