When a piston generates a sinusoidal wave in the tube, the new volume of the air originally located between x1 and x2 becomes

2-3 Traveling sound waves
Additional material - Derivation of displacement and pressure amplitudes formula


Consider a tube of cross-sectional area A. The volume of air located between positions x1 and x2 is





Using                    and

Let us take the limit when x2 becomes very close to x1

 From the definition of the Bulk modulus

Thus the change in volume ΔV due to the sound wave is