The Listening Room: Your Final Component - Part One

Room Integration 101

You’ve spent years researching! You’ve read all the magazines and books, gone to all the trade shows and tried to listened to as many different systems and components in other peoples systems and in showrooms as your time allowed. You’ve done everything humanly possible to compile your short list of components. You’ve traveled nearly the circumference of the moon in an attempt to hear everything on that short list of components in conditions that will closely resemble your own. You’ve dragged home loads of heavy amplifiers, large bulky speakers and assorted black boxes - let’s not even go into all the cables - to assemble just the right synergy. But what about the room in which all that time, energy and expense has been finally assembled. What? You’ve never given that any real thought! OK, back to school we go.

Frequency and waves

To understand how the listening room imposes its vast and sweeping signature upon our reproduce music, we must look at some technical issues. All you who feel mathematically challenged, don't panic! I will contain the necessary number crunching to simple "old" math techniques, all manageable with a simple calculator. But we need to understand some basic terminology first.

Sound is described by the Oxford American Dictionary as, " the vibrations that travel through the air and are detectable (at certain frequencies) by the ear." It is also important to understand that sound propagates in all directions from its source unless prevented form doing so by the presence of something, very much like the ripples or waves that are produced when you throw a stone into a pond. That analogy is less than perfect because with the pond, propagation is only two dimensional, radiating in a circle from the point of generation, while sound propagates spherically form the point of generation.

When we speak of sound we most often are speaking in terms of frequency. An audio signal is a complex combination of alternating periodic (occurring at regular intervals) signals called sine waves. The frequency of the signal refers to the number of repetitions (or cycles) which are completed in one second. The greater the number of cycles completed in one second, the higher the frequency. This leads us to the wavelength. One wavelength is described by the distance covered during the period of one complete cycle, regardless of frequency.

Now let's look at an example. Start with the lowest frequency attributed to the range of human hearing, 20 cycles per second, or 20 Hertz (Hz). The term Hertz was adopted in 1960 by an international group of scientists at the General Conference of Weights and Measures in honor of Heinrich R. Hertz, a German physicist born in 1857. Heinrich opened the way for the development of radio, television and radar with his discovery of electromagnetic waves during research done between 1886 and 1888.

If the frequency of the sound is 20 cycles per second, that means that in one second, our cycle occurs twenty times. Sound is given as propagating through air at 772 miles per hour, or the more usable value of 1132 feet per second. This propagation standard is based on the air pressure at sea level (14.7 pounds per square inch) and at a standard temperature of 74 degrees Fahrenheit. So if we take one second of propagation (1132 feet) and divide it by 20 Hz, which is the frequency we are examining, we see that one cycle or wavelength at that frequency is 56.6 feet long! Performing the same computations with the highest frequency attributed to human hearing, 20,000 Hz yields a wavelength of just .68 inches!

If you're reading between the lines here you may have gathered that in order to fully support a 20 Hz note, you would need a room at least 56.6' long! Good luck! Since sound waves propagate at a fixed velocity, the distance between the source (your loudspeaker) and you the listener would need to be at least one full wavelength in order for that 20 Hz note to fully develop. A good example of this effect is demonstrated by some of these booming car stereos, from which the bass frequencies often precede your sighting of the vehicle.

Since few of us have rooms over 60 feet long, we can make up for this with a principal know as modulation. This is why so many believe in the use of sub-woofer. A sub-woofer is a dedicated speaker that only reproduces frequencies below a certain threshold, typically the two lowest octaves (From 20 to 80 Hz) or lower. The subwoofer modulates a sufficient amount of air in our listening room to excite other senses in our bodies that reinforce our perceptions of the lowest frequencies.

Acoustic sound waves are what are called traveling waves. That is, they propagate from one place to another at a fixed rate of speed. This takes time. If the distance from the source to our ears is large, there will actually be a very obvious time delay before we hear the sound. That's why you see the flash of lightning before you hear the sound of the resultant thunder. Growing up, I was taught that I could determine how far away a lightning flash was actually occurring. After seeing a lighting flash, I would start counting. When the thunder began, I would divide the number I had counted to by five (5280 feet in a mile, 1132 feet per second yields approximately 5 seconds per mile) and the result was the number of miles between the lightning flash and me.

Interference occurs when two or more propagating waves arrive at the same physical location in such a manner that they cancel or reinforce each other. Those locations, or nodes, where these interference’s occur is a function of wave length as it applies to their phase relationships.

Let's go back to our pond analogy for a moment. What happens if we drop two identical stones into our pond at the same time at two different spots? When one wave encounters the other, they create areas that either splash or null. Propagation continues, but obviously the wave characteristic gets modified. The splashes are caused by constructive interference, while the nulls are created by destructive interference.

Constructive interference refers to the condition present when traveling waves, which are of the same frequency, interact and they are in phase, meaning that the troughs and peaks of the waves coincide. The amplitudes of the waves sum and cause a peak (splash).

Destructive interference, often called suck out, occurs when traveling waves, which are of the same frequency, interact and are exactly 180 degrees out of phase, meaning that the trough of one wave coincides with the peak of the other. In this case, the summing of their amplitudes yield a null condition. The waves cancel each other entirely, effectively resulting in no sound.

Standing waves, created by the physical limits of our listening room, are created when a traveling wave encounters a perpendicular reflective boundary such that the reflected wave constructively reinforces the propagating wave. This creates a stationary wave pattern, consisting of an alternating sequence of nodes formed when the waves pass through each other in opposite directions. At specific frequencies determined by our room’s dimensions, these compressions and rarefactions occur simultaneously at the opposite boundary surfaces, reinforcing the wave from both directions. A standing wave therefore is essentially a resonant condition which occurs when the zones of compression and rarefaction are stationary during the resonant period (of course the waves aren't really stationary, just the subsequent nodes due to the coincidence of wavelength and dimension). The condition occurs specifically at frequencies where the physical distance for the radiating surface to the reflective surface is equal to a multiple of 1/2 the original wavelength of the propagating sound wave. The result is a resonant condition that is uncontrolled and requires little energy to sustain. This creates a large peak in the frequency response which can be very difficult to suppress.

Why is all this stuff important? Because knowing these things in combination with the dimensions of your chosen listening room will allow you to determine which frequencies are going to give you trouble and which ones are not. Let's look into that relationship.

Your room

In a rectangular room, the three dimensions (height, width and depth) determine the three primary sets of standing waves. If any two dimensions are the same, it provides more reinforcement for that resonant frequency. A cube provides the worst case scenario. It will have one primary resonance with a tremendous peak due to reinforcement form three identical wave fronts. Since we can't get rid of these resonance's (there are ways of taming them slightly though, more on that next month), we have to approach the problem by selecting an available room with the best overall dimensions.

Since we will hopefully be working with three different dimensions, we will have three primary resonant frequencies to deal with. If we could have absolute control of the dimensions, it would be nice to be sure that none of the standing waves could affect any of the others generated in our room. Unless you are building your own house or adding on a listing room, this is pretty tough to do. But you can analyze the dimensions of the available rooms in your home.

Two theories exist on the choice of proper dimensions, the golden ratio and the one-third octave principals. The first option is based on the age-old golden ratio first discovered and codified by the ancient Greeks. It is a dimensional ratio of 1 to 1.6. Using an real world standard of an 8 foot ceiling as the 1 in our ratio, the ideal room under this theory would be 12' 10" wide by 20' long with an 8' ceiling. Southern Maryland Irregular HAL has built his house around a room with almost this perfect ratio – 16"W x 26"L x 10"T. As I mentioned, this is the oldest solution to the standing wave problem and is certainly much better than a cube, but can allow for unintentional harmonic reinforcement at numerous mid-bass and mid-range frequencies.

The second theory has gathered much more appeal as it limits compound reinforcement throughout the audio spectrum by overlapping reinforcement in 1/3-octave increments. Reinforcement in thirds does not permit any even order reinforcement, thereby generating the least amount of summing throughout the audio spectrum. The ratio here is 1 to 1.25 to 1.6. Using this set of ratios and imposing our 8' ceiling limit as the 1 yields a relatively smallish room of 10' wide by 12' 8" long by 8' high. While this may be great for standing wave control, try to get any significant bass out of a room this size!

On a positive note, any one of our dimensions in the one-third ratio can be halved or doubled without changing the one-third octave relationship and without seriously changing the overall smoothness of the room's bass response. Thus a 10’ W x 25’ 6" L x 8’ T room would be quite effective. But again, not a terribly likely dimension!

Whatever you think of either set of ratios, using them is difficult unless you have the luxury of building your own room, as I have stated. What is useful is knowing how to calculate the reinforcements in your real world room and, when possible, taming those accordingly.

Measure your rooms dimensions, front to back, side to side and top to bottom to the nearest inch and convert the dimensions to feet only (i.e., 12' 10" = 12.8 feet). The primary (fundamental) axial resonance for any dimension will occur with a wavelength that is exactly twice any room dimension. Since we have developed a constant for the propagation of sound waves (1132 feet per second) and we know that the condition occurs specifically at a multiple of 1/2 the original wavelength, we can use one half of that number, or 566 feet per second. Dividing 566 by any room dimension gives the center frequency of that dimensions lowest full length standing wave. Obviously standing waves will also occur at even multiples or divisions of that frequency as well, but with less affect than the fundamental. So, a 12 foot long room will experience its lowest full wavelength axial resonance at about 47.16 Hz (556/12'). Armed with this information, you can now determine the primary resonance for the three major dimensions in your chosen listening room.

The reason I’ve gone through all this is to get you to think about the room you will use for your (dedicated?) listening room. A small 8" x 8" x 8" room should be avoided like the plague! If you have a couple of rooms that you MIGHT use, do the math before selecting one over the other. Often there are other considerations which must be taken into account, but, given that you now know the listening room is your most important and overlooked component, you are prepared to make the correct sacrifices. Choosing the room with the least amount of "bad vibe" will save both energy and money when we try to tame those problems later.

Room Integration 102 - Further reading for the ardent student

Rather than try to paraphrase and expand on what has already been covered in great detail on the web at two outstanding sites, I’m just going to point you towards them. The first is located on the unique looking site for Cardas Audio. The second is the very informative Hales Design Group University site. Recommended reading for all undergraduates, and great refresher material for all you upper classmates!

When you’ve finished all this homework, you’ll be ready for next months 201 course on reflections and room treatment. Be sure to study and take notes, I’ve heard this instructor likes pop quizzes!

...Greg Weaver
gregw@soundstage.com

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