In the context of sound waves, the restoring force refers to the force that acts to bring a disturbed medium back to its equilibrium position. It is the force that opposes the displacement caused by the wave and allows the medium to oscillate around its equilibrium.
In a sound wave, the restoring force is primarily due to the elasticity of the medium through which the wave is propagating. When a sound wave passes through a medium, it causes compressions and rarefactions, which are regions of increased and decreased pressure, respectively.
For example, in a longitudinal sound wave traveling through air, when a compression occurs, the air particles are pushed closer together, resulting in an increase in pressure. The restoring force in this case is provided by the elastic properties of the air molecules, which tend to push the compressed air particles back to their original positions, thus restoring the equilibrium state.
Similarly, in the rarefaction region of a sound wave, the air particles are spread farther apart, resulting in a decrease in pressure. The restoring force now acts to pull the rarefied air particles back towards their original positions.
The presence of this restoring force allows the disturbed particles of the medium to oscillate around their equilibrium positions, creating the characteristic vibration and propagation of sound waves.