Superposition of plane sound waves

The pressure fluctuation is given by

cos(kx - ωt) + R cos(kx + ωt)

which is a combination of plane periodic waves travelling in the positive and negative x directions.

Notes

In each movie below the upper panel shows the pressure fluctuation as a function of x and the lower panel shows the corresponding fluid particle motions.

Each minimum in the pressure correponds to a minimum in the fluid density and the particles are far apart.

Each maximum in the pressure correponds to a maximum in the fluid density and the particles are close together.

R = 0

This is a plane wave travelling in the positive x direction. Each fluid particle oscillates with the same amplitude. However, the phases are different and this gives the illusion of motion through the fluid.

R = 1

This is two plane waves of equal amplitude travelling in opposite directions. The motions combine to give a standing wave. All fluid particles oscillate in phase but the motion amplitudes vary with x.

R = ½

This is two plane waves of unequal amplitude travelling in opposite directions. The motions combine to give a wave that combines the features of travelling and standing waves.