Acoustics for diy folks!

In the following, I have included descriptions of basic phenomena that should be known by sound diy folks.

Sound emerges because air molecules are excited into oscillation around their equllibrium position. Unlike what many people think, the molecules does not travel through the air, they are quasistationary positioned. The speed of sound is the travelling speed of the sound, and this exact figure is a product of the stationary pressure, the humidity and the temperature, but for normal atmospheric conditions, the expression can be simplified to:

v = 331 m/s + (0.6 m/s)*T[C]

From this it can be seen that in normal living room conditions (T=20 Celsius) v is 343 m/s.
A temperature of Celsius means that the speed of sound is: m/s

The wavelength of sound waves depends on the frequency and the medium in which the wave travels. In air (at 20 Celsius) during normal atmospheric conditions the wavelength, lambda is given by the ratio:

lambda = 343 / f

Diffraction the bending of waves around obstacles and the spreading out of waves beyond openings.
The fact that you can hear sounds around corners and around barriers involves both diffraction and reflection of sound. Diffraction in such cases helps the sound to "bend around" the obstacles. The fact that diffraction is more pronounced with longer wavelengths implies that you can hear low frequencies around obstacles better than high frequencies.

Standing waves

A standing wave is a resonance condition in an enclosed space in which sound waves traveling in one direction interact with those traveling in the opposite direction, resulting in a stable condition.
This is also known as constructive interference. Destructive interference occurs when the waves are 180 degrees out of phase.

Constructive interference.

Destructive interference.

By clicking here, you can calulate the number of standing waves (room modes) in a cubic shaped enclosure.

Radiation from a baffled piston

A circular piston in a large baffle is a good starting approximation for investigating the radiation of sound from a loudspeaker mounted in an enclosure. The far-field pressure radiated by a baffled piston depends on the radius of the piston a, the frequency and the direction (with 0 being directly in front of the piston) according to the formula:

At low frequencies

(when ka is small) a loudspeaker radiates sound in all directions. This behavior is primarily the reason why the location of a subwoofer doesn't really matter regarding the on-axis location- you can place it anywhere and it will still fill the room with sound.

Radiation of low frequency sound.

3D omnidirectional radiation pattern.

At medium frequencies

As the frequency gets higher, but assuming the speaker diameter does not change, the value of ka increases and the speaker becomes directional. That is, the sound energy produced by the speaker becomes channeled into a preferred direction and very little energy is radiated at other directions. The radiated sound is pretty much contained within a cone of 55 from the center axis. The radiated sound field is strongest right in front of the speaker and weakens as you move to either side

Radiation of medium frequency sound.

3D radiation pattern.

At high frequencies

When ka becomes much bigger than 1 the sound field radiated by the loudspeaker becomes narrower and side lobes appear. Now the main lobe of radiated sound is limited to about 20 on either side of the central axis, and the pressure amplitude falls off rapidly as you move away from the central axis. Notice that the sound waves in the side lobes have the opposite phase as the sound wave in the main lobe and the side lobes have significantly lower amplitude than the main-lobe.

Radiation of high frequency sound.

3D radiation pattern.