# Details of sound waves

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?

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
$$\Delta P = P_2-P_1$$
$$\Delta P = P_2\left(\frac{V_1 - V_2}{V_1}\right)$$
$$\Delta P = -\frac{P_2}{V_1}\Delta V$$