Introduction
In our last article on home theater layout, we spent some time looking at the video issues affecting the room. In this article, we will look at the audio issues that can influence room layout and speaker configuration.
Room Modes
When it comes to audio, there are important relationships between the room’s length, width, and height, and the way your room sound. For home theater, some combinations should be avoided. This is because of what is known as standing waves. If the wavelength of a particular tone happens to be a multiple of the distance between two opposing walls (or ceiling and floor), that wave will be reflected back and forth between the two walls. It will be reinforced relative to other tones, and also tend to hang around long after other tones have died out. The frequency at which this happens is called a room mode. This particular case of standing wave is called an axial room mode.
If the wave is reflected around the room in a single plane via four walls (or two opposite walls, the ceiling, and the floor), this forms a tangential room mode when the total distance of this trip is a multiple of the wavelength of a tone. Tangential room modes also increase the relative level of affected tones, but only about half as much as axial modes.
Waves can also reflect around the room via each surface in the room, i.e. four walls, the ceiling and the floor. When the total distance of this round trip is a multiple of the wavelength of a tone, we get an oblique room mode. Oblique room modes reinforce affected waves only about a quarter as much as axial modes. 
Room modes are not a big issue for higher frequency waves, because many thousand different frequencies will fall into this category, and they all tend to blend together to form a homogeneous sound. This is not the case with bass frequencies below about 300 Hz, however. At these frequencies, the room modes are pretty isolated, and once excited, can lead to certain frequencies sounding boomy and muddy. Now you can begin to see why certain dimensions of rooms should be avoided. A cube would be the worst, since the same few bass frequencies would be reinforced between each axis, leading to annoying boominess for sure. The next worse layout would be a room where any two dimensions were the same, e.g. a square room.
Dealing with Room Modes
There are few ways to deal with room modes. The first is through careful design. It turns out that there are certain dimensional ratios that result in a fairly even distribution of modes at the low frequency end of the audio spectrum. Sometimes referred to as golden ratios, these dimensions were researched by L. W. Sepmeyer. There are many ratios which give good results in this regard, but three popular ratios shown in Table 1. 
In the post construction phase, we can use acoustical treatments to combat the harsh effects of room modes. These include broadband absorbers, such as foam absorbers, traps, and even furniture; and tuned absorbers, such as bass traps and Helmholtz resonators.
While it is possible to place acoustical treatments by guess and experience, it is best to have the room acoustically analyzed to first determine the extent of the need for treatment, and during the treatment process, to see exactly what effect the treatment is having on the room. Sometimes, even minor repositioning of a speaker can have drastic effects on the quality of the audio at the main listening position, and may stem off the need for elaborate room treatment.
Speaker Layout
Nowadays, the typical home theater speaker layout is either a 5.1 layout, or a 7.1 layout. Since 5.1 can be considered a subset of 7.1, we will mention it only in the context of discussing 7.1 layouts.
Dobly Digital Surround is considered to be a 5.1 surround format because it has five discrete channels of audio (front left, center, front right, surround left, surround right) plus a low frequency effects (LFE) channel. Dolby Digital EX is exactly like Dolby Digital Surround, with the addition of a matrixed mono surround back channel. Because this additional channel is not a discrete channel, calling it a 6.1 format has been discouraged. Many home theater receivers however, send this mono channel to two separate amplifier channels, named surround back left and surround back right. Thus we now have seven speakers plus a subwoofer to be placed in the home theater room. Some people call this arrangement 7.1.
Dolby Digital EX
Not surprisingly, there are different recommendations from the developers of the current home theater audio formats regarding speaker placement. Dolby Laboratories, (which developed Dolby Digital EX together with Lucasfilm THX) has the following recommendations for setting up the speakers for a “7.1” scheme. 
The center speaker should be in the center of the screen. For a front projection setup, it is best to put it behind the screen. Otherwise, above the screen is better than below the screen.
The left and right front speakers should be between 22 and 30 degrees off the screen center, and at ear level.
The surround left and right speakers should be between 90 and 110 degrees from the listening position, and about 2 feet above ear level.
The surround back left and right speakers should be between 135 and 150 degrees from the listening position. They should be about 2 feet above ear level.
The low frequencies produced by the subwoofer are typically non-directional, so theoretically, the subwoofer can be placed anywhere in the home theater room. Practically however, note that a subwoofer that is placed on the floor along a wall will be 3 dB louder that if were not on the floor. And a subwoofer placed in a corner will sound 6 dB louder. This can lead to a boomy bass sound on certain frequencies.
THX EX
The THX recommendation for speaker placement is a little different from Dolby.
The left and right front speakers should be about 23 degrees off the screen center (i.e. 46 degrees included angle).
The surround back left and right speakers should be placed next to each other, directly behind the listening position, if the digital decoder has THX ASA (Advanced Speaker Array) decoding. Otherwise, these speakers should be placed as for Dolby recommendations. They should be about 2 feet above ear level.
THX recommendations for other speaker placement is the same as the Dolby recommendations. Note however, that THX insists on dipoles for the surround left and right speakers, and insists on monopole speakers for the surround back channels.
Conclusion
With the right set of modern home theater audio decoders and amplifiers, it is possible to get very good sound to accompany your video. Coupled with a properly laid out and treated room, and a set of high quality speakers configured to match your decoder, you will get awesome sound. Together with the proper video display, your home theater will give years of delightful entertainment.