Flat acoustic wave

Professional Definition

A plane acoustic wave is a wave whose front (a surface with the same phase and amplitude) is a plane perpendicular to the direction of sound propagation.

In physical terms, this means that the acoustic pressure and the velocity of particles have the same values across the entire cross-section of the wave. Mathematically, these quantities depend solely on the distance from the source and time, not on the up-down or left-right position.

Although an ideal plane wave is a physical abstraction, in engineering practice it is adopted as a model for sound propagating in waveguides (e.g., pipes, ventilation ducts) below the so-called cutoff frequency. Importantly: in contrast to a spherical wave, a plane wave (theoretically) does not lose energy with distance due to geometric spreading.

Acoustics in Simple Words

Imagine a piston perfectly fitted to the inside of a very long pipe. When you push it forward abruptly, you will uniformly compress the air in front of it across its entire surface.

This zone of compressed air will move deeper into the pipe like a moving wall. It doesn’t matter whether you measure the pressure right in the middle of the pipe or just along its wall – at a given point in the cross-section, the value will be the same.

This is what a plane wave is: a sound that does not "bulge" sideways like a balloon (spherical wave) but marches forward uniformly, like soldiers in perfect formation passing through a narrow canyon. Because the energy is "trapped" in the pipe and cannot escape sideways, the sound in this model can travel very long distances without significant weakening.

Summary

• Directionality: Energy does not disperse in space but travels precisely in one direction.

• Constant energy: Under ideal conditions, the loudness of a plane wave does not decrease with distance (no geometric losses).

• Application: A key model in the design of noise silencers, analysis of exhaust pipes, and air conditioning and ventilation systems.