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We show that the macroscopic quantum beats of the magnetization can be produced by using a sound wave in a free single-molecule magnet. Employing the rotating wave approximation and a numerical method, we derive the Hamiltonian of a rotated two-state spin system and present superpositions of spin and rotational states. A parameter involving the energy gap and the moment of inertia plays an important role in determining the shape and the period of the quantum beat. Also, such a beat structure is governed by the total angular momentum and the coupling of the single-molecule magnet to the substrate. The condition for a pronounced beat with a large period is discussed.