Sound is generated by compressing air molecules such as a speaker moving back and forth like a piston, pushing and pulling on the air to produce waves. Sound uses air or other mediums in which to travel. Since air compressions require energy to create them, to get rid of them, we must convert the acoustical energy into something else. Bass vibrating the walls of a living room is a good example.

In acoustics, we use open-cell foam panels or fiberglass bating. These panels work by allowing air molecules to penetrate and, as the energy flows over the many surfaces, convert the energy into heat. Thermal dynamics is the science, sound absorption is the result. As one can imagine, lower frequencies require significantly more energy to generate than high frequencies. Think of the sound from an elephant as opposed to the sound of a mouse. It follows that absorbing low frequencies is much more demanding than high frequencies. As a result, high frequencies (short wavelengths) are typically a piece of cake to absorb while low frequencies (long wavelengths) get all of the engineering attention.

How low and how long?
To calculate the size of the wavelength, you simply use the speed of sound (1100ft/sec) and divide it by the frequency. For example, 1000Hz is calculated by dividing 1100/1000=1.1ft or about 13 inches. Super low bass like 20Hz is 1100/20=55ft (55 feet long!) Does this mean that we need 55 ft of acoustic material to absorb 20Hz? No. Anachoic chambers typically use 4 ft or 5 ft wedges to absorb low frequencies and they do it by using the following math.

Speed of sound:	1100 feet per second
	÷
Frequency:	1000 Hertz
	=
Wavelegnth:	1.1 ft

If you consider a loudspeaker, like a piston, it begins by pushing air outwards. It then comes back to the center and goes inward. This creates air presure compressions (high presure zones) and rarefaction (zones of low presure) we perceive as sound waves. Because the loudspeaker begins a cycle by first pushing on the air, most of the kinetic energy is generated in the 1st quarter of the wavelength as the speaker pushes outwards. This is the 1st key to solving the acoustic absorption mystery.

The 2nd key is the knowledge that sound rarely comes from a single direction. In fact, once it is airborne, it comes from many angles. This being the case, we can figure that in fact most of the energy is striking the panel at some angle (the angle of incidence). A 3" thick panel, laid across an 8ft wall, will absorb 8ft wavelengths at the extreme angle of incidence. For simplicity, we divide the ¼ wavelength in half, resulting in 1/8 of a wavelength.

The bottom line.
Divide the speed of sound by the frequency and then divide the answer by 4 to get the quarter wavelegnth. Divide that result by 8 to get the angle of incidence wavelegnth. This is the math used to specify the thickness required to effectively absorb a target frequency.