Ct is the heart of the TAC engine. It acts something like a transistor oscillator, in that it teeters back and forth thermally, taking up energy from the working fluid, then giving it back, thereby keeping the oscillation going. This permits resonator design variations not restricted by a set geometry. Thermal energy migrates through the working fluid from HXh to HXc in the form of a rapidly moving wavefront, a pressure wave, or shockwave. This is the acoustic component, a pressure wave moving through an elastic medium.
Lightning is a good analogy.
An electric arc cutting through the atmosphere superheats a channel of air, and the resulting explosive expansion of atmospheric gases produces a shockwave that is commonly called a thunderclap. The traveling acoustic pressure wave carries with it the thermal component that produced the wave. In other words, it transports the heat of the lightning bolt, diffusing it to the surrounding atmosphere. A similar phenomenon takes place inside a TAC engine. Like water in a wavepool, the acoustic pressure wave sloshes back and forth inside the resonant cavity, being alternately heated and cooled, the pressure component ballooning and contracting repeatedly.