Using Andreev and Lifshitz's supersolid hydrodynamics, we obtain the propagating longitudinal modes at non-zero applied pressure P_a (necessary for solid 4He), and their generation efficiencies by heaters and transducers. For small P_a, a solid develops an internal pressure P ∼ P_a^2. This theory has stress contributions both from the lattice and an internal pressure P. Because both types of stress are included, the normal mode analysis differs from previous works. Not surprisingly, transducers

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... are significantly more efficient at producing elastic waves and heaters are significantly more efficient at producing fourth sound waves. We take the system to be isotropic, which should apply to systems that are glassy or consist of many crystallites; the results should also apply, at least qualitatively, to single-crystal hcp 4He.