Details of sound waves

Question

I am a high school student, and I am very confused about sound waves. My teacher taught me that sound is a pressure wave, i.e the atmospheric pressure varies during the propagation of sound, and all the medium particles perform simple harmonic motion (if amplitude is not so high).

But my confusion is that if all the particles undergo simple harmonic motion in the direction of propagation of sound, what is the restoring force which is acting here? If it is the attractive forces between the molecules then is it necessary that it acts opposite to displacement?

Answer 1

The restoring force here would be the fact that gasses always seeks to equalise pressure. Thus, when a sound wave moves around some particles, the pressure of the surrounding particles will eventually get the system back to rest.

Answer 2

Consider a localized volume or "bubble" of an ideal gas ($V_1$) at a pressure $P_1$. Something happens to compress that bubble isothermally to a new volume $V_2$. What would be the new local pressure of the bubble? $$ P_1V_1 = P_2V_2 $$ $$ P_1 = \frac{P_2 V_2}{V_1} $$ So

$$ \Delta P = P_2-P_1 $$

$$\Delta P = P_2\left(\frac{V_1 - V_2}{V_1}\right) $$

$$\Delta P = -\frac{P_2}{V_1}\Delta V $$

A change in pressure is proportional to a restoring force, and the restoring force here is directly proportional to the local change in volume.