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You want to look at such things in terms of the response of the medium, not the initial shock. If I toss a rock in a pond, the impact is non-periodic, but the response of the water in the pond generates a wave train. Same if I pluck a guitar string. The initial motion deforms the solid which acquires kinetic energy. The undisturbed portion of the solid strains as it absorbs the kinetic energy from the adjoining material, then releases the strain energy causing more of the solid material to move. The cycle repeats producing the wave train. Because energy is dissipated all the waves in the the train aren't identical, but their frequency is about the same, at least in a linear material.

Christopher Wright P.E. |"They couldn't hit an elephant at
chrisw(--nospam--at)    | this distance" (last words of Gen.
...................................| John Sedgwick, Spotsylvania 1864)

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