Why solid makes sound upon hitting? When we hit any objects it vibrates and makes sound. my question is why it vibrates? what happens in the quantum level?
 A: Here is a simplified answer.
Let's say you strike a piece of wood with a hammer. The hammer possesses kinetic energy and momentum and some or all of these will be transferred to the wood, a process which begins the instant that they touch.
Since all of their atoms and molecules have bound clouds of electrons encircling them, those clouds repel one another as the hammer begins to press into the wood. The wood molecules get pushed on by the hammer atoms and because those wood molecules are surrounded by other molecules, the next layer of molecules experiences the repulsive force of the first layer, and the motion of the hammer is thus propagated into the bulk of the wood.
(Of course, the exact same process occurs inside the hammer face, but it is made to be resistant to deformation and so the wood experiences most of that).
Note that because those molecules possess mass, and are being acted on by the elastic forces provided by the interactions of the electron clouds, the bulk of the wood will support the propagation of fast-moving displacement waves throughout it. Some of these waves get propagated straight out into the surrounding air and you hear the impact sound. Some of them get propagated into the inside of the wood and bounce around there. Each time one of these waves bounces off the surface of the wood and heads back into the interior of the wood, some of the energy in the wood wave leaves the wood as sound waves in the air, and you hear these too an instant after you hear the initial impact noise.
A: You ask:

why it vibrates? what happens in the quantum level?

I will quote from this book's chapter  abstract to see how complicated the answer is:

Optical Properties of Ions in Solids pp 107–185Cite as
Quantum theory of Lattice Vibrations     R. Orbach


Part of the NATO Advanced Study Institutes Series book series (NSSB,volume 8)
Abstract


The quantum mechanical theory of lattice vibrations in solids is reviewed and summarized. The formalism is developed first in the classical manner, and the various symmetries of the normal mode eigenvalues are discussed. The transition to the quantum mechanical formalism is done by introducing operator forms for the appropriate physical (observable) quantities. As an extension of the quantum mechanical formalism, the thermodynamic properties of the lattice vibrations (entropy, free energy, etc.) are investigated. An extensive treatment of critical points in the phonon density of states is given; this includes a discussion of the so-called Van Hove singularities, and a cataloguing of the types of singularities involved. Finally, the lattice vibrational equation of state is formulated, and the effects of the boundary conditions on the frequency distribution are discussed.

