Air gap or not, that's the question

When it comes to sound absorption panels, the question whether to install them directly on the wall or leave an air gap behind often come up. Is there a difference? If so, what is it?

If we take a close look at air as a medium transferring sound energy, we can think of air particles as a group of same-polarity magnets inside a container (the room boundaries). The particles are in balance due to the intermolecular forces between them.

When a particle is displaced, the movement will cause displacement of the particles around it, on and off axes, in all directions to regain this balance. That’s how sound vibrations propagate in 360 degrees.

The spacing between particles is affected by the pressure they’re under. The higher the pressure the closer together they are. On earth, we all experience atmospheric pressure. Which is, basically, the weight of the entire column of air above. The atmospheric pressure is about 101KPa.

The movement of a sound source will force the air particles near it to cramp together, which increases the atmospheric pressure in that area. This pressure change in atmospheric pressure due to sound is very small. For example, it is +-0.00002Pa at the threshold of hearing. To put it in perspective, that is approximately 28 million times smaller than the pressure a medical syringe can make. But, so long as these pressure changes are cyclic; meaning it follows repetitive cycles between the start value up to a max value, down to a min value and back to start, then our brains can detect it, and we experience the “sensation” of sound.

A sound source generates periodic bursts of energy. The movement of the source sets the particles near it in motion, increasing its velocity and kinetic energy. As the particles move closer to each other and compress, the atmospheric pressure increase causing them to slow down and their kinetic energy converts into elastic energy; until the particles can not compress anymore, under that pressure. At that moment, the particle velocity become zero and all the kinetic energy is stored as elastic energy. this elastic energy starts moving the particles in the opposite direction and they gain velocity and kinetic energy in that direction as they move apart from each other. This decompression translates into reduction of the atmospheric pressure until the particles can not decompress any more and at this point they again have zero velocity and maximum elastic energy which starts compressing them again and the cycle keeps happening back and fourth

Each time this cycle happens, some of the energy conversion is lost, until eventually all of it is dissipated and the sound is gone.

Fibrous absorbers work by restricting the air movements which convert the sound energy into heat via friction. The absorption of energy is most effective when the particles are in maximum elastic energy status right before that energy is converted to kinetic energy, which continues the state change cycle. It is very clear from the pressure vs time chart that if the absorber is placed at a distance equal to ¼ wavelength (or ¾ wavelength) then it will have the most impact on this wave. In other words an absorber with a certain thickness will have 100% absorption of all the frequencies of which their ¼ wavelengths fall within the thickness of the absorber. Moving the absorber away from the wall will shift it's impact towards lower frequencies since the ¼ wavelengths of low frequencies is further away from the wall.

The chart below is showing the absorption coefficient for a 2" absorber with (green line) and without air gap (blue line). The 80% absorption frequency range is shifted down from 950Hz to 450Hz.