The wavemaker theory for a single layer fluid is a classical chapter of books on water waves. Indeed, linear waves with a desired amplitude, wave length, and frequency can be generated with the horizontal motion of a vertical plate, which is estimated from the wavemaker theory. However, there is much less work on the wavemaker theory when two fluids are superposed. Here we consider a variant of the classical wavemaker theory, which consists in a semi-infinite container with two layers of fluid of finite depths, bounded above by a rigid roof and on one vertical side by a piston. The lower fluid is incompressible (typically a liquid) and the upper fluid is a lighter gas (or liquid), which is considered to be incompressible as well. When the piston is set in motion, waves are created at the interface between the liquid and the gas. Resulting wave profiles and velocity fields based on linearized theory will be shown and compared to the classical one fluid wavemaker theory and to numerical simulations of wave generation with two layers of fluid. Two approaches will be presented, a stationary one, which is the equivalent to the wavemaker theory encountered in books in the case of a single layer, and the initial value problem that takes into account the transient motion from water and wavemaker at rest. The effects of both the density ratio, as well as the effects of the rigid roof are analyzed.

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