Question

how sound is propagated through a medium by the change of density

Answer 1

through vibration the particals pushes the next one to propagate

Answer 2

Sound can propagate through a medium such as air, water and solids as longitudinal waves and also as a transverse wave in solids (see Longitudinal and transverse waves, below). ... The behavior of sound propagation is generally affected by three things: A complex relationship between the density and pressure of the medium.