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Old 04-29-2008, 11:02 PM   #2
Big Daddy Big Daddy is offline
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Jan 2008
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I exceeded the number of characters allowed in my original post. Therefore, I moved some of the information here.
Example: If the room has a length of 5m, then the resonance frequencies of the first five room modes are: 34.3Hz , 68.6Hz, 102.9Hz, 137.2Hz, 171.5Hz .

Response of the One Dimensional Room as a function of Source Location

In the animations below, the red dot represents the source as it moves from the left wall (at x=0) towards the right wall (at x=5). The sine curve in the animation represents the amplitude of the pressure wave as a function of position in the room.

Driving the room at a resonance frequency

As the source moves along the length of the room, the resulting room response (as indicated by the amplitude of the pressure standing wave pattern) is a maximum when the source is located at an antinode for that given frequency. Notice that when the system is being driven at a resonance frequency the pressure amplitude is always greatest at the walls of the room. Furthermore, the maximum pressure is twice (2) the source amplitude, because the incident and reflected waves are in phase at the wall boundaries. When the source is placed at a node for that frequency standing wave pattern, the maximum room response drops to zero at that frequency. With a speaker located at a node, the room will be "dead" no matter how loud the speaker is. Moving the speaker a small distance away from the node brings back the room's response

Mode 1 (34.3 Hz)

Mode 2 (68.6 Hz)

Mode 3 (102.9 Hz)

Animations courtesy of Dr. Dan Russell, Kettering University

Driving the Room at a Frequency which is Not a Resonance Frequency

Standing wave patterns only occur when the room is being driven at a resonance frequency. At any other frequency, the pressure waves radiating outwards from the source reflect from the walls, but do not combine to produce a standing wave. As a result, there are no nodes and antinodes, and the pressure can go to zero at a wall. The maximum pressure never exceeds the source level (1) and the location of the pressure maximum moves with the source.

Driving frequency = 51 Hz

Animations courtesy of Dr. Dan Russell, Kettering University

Even Number of Subwoofers Works Best
Two or four subwoofers deliver the greatest benefits in smoothing out irregular bass for multiple listening seats. According to Todd Welti, an associate of Dr. Toole’s, whose white paper, "Subwoofers: Optimum Number and Locations," explored in detail multiple subwoofer performance: “The conclusion I came to was that two subwoofers give you about 90% of the performance that is possible, and that four take you about as far as you can reasonably expect to go. Anything more than four is not going to get you much in the general sense -- and these are general conclusions.”


In a square or rectangular room, the center of the room is the worst location for the listening chair or for the subwoofer. I am not an artist. The following diagrams only demonstrate the best positions for the subwoofers. Ignore the position of the listening chair. That is just bad drawing.

Diagrams Created By Dig Daddy

Stacking Two Subwoofers Versus Placing Them in Different Locations
If you stack (co-locating) two subwoofers on top of each other and place them in a corner, you will get up to 6dB's of additional output. If you place the two subwoofers in different locations (e.g., the middle of the two side walls or one in the middle of the front wall and the other one in the middle of the rear wall), you may not get as much additional output, but two subwoofers on two sides of the room will eliminate many room modes and create a more even and smoother bass across the room for all listening positions. The advantages of placing two subwoofers in different locations far outweigh any additional output that you may gain from stacking them on top of each other. Read THIS interesting post on stacking subwoofers. There is more information on stacking HERE.


Todd Welti at Harman International:
You shrink the whole room by 25% and put the subwoofers at the corners of that virtual room. Of course you get incredible performance, but that is not practical for most people. But if you use two or four subwoofers in the corners or the wall midpoints, you can get pretty good performance.
Under this solution, low frequency support is compromised a bit in mid-wall placement, in favor of a flatter overall frequency response.

Dr. Floyd Toole:
That said, no matter how many subwoofers and how many listeners we’re talking about, equalization should be the final step to make it sound right. A single subwoofer can entertain a single listener with equalization -- good sound is possible. But once you have more than one listener, then you need multiple subwoofers.
Based on his experiments with subwoofer placement, Dr. Toole recommends that it is easier to place subwoofers in corners and equalize out the room modes, than to try and avoid the modes and sacrifice low frequency support in favor of a flatter overall response without EQ. Corner placement adds to the overall SPL of the subwoofer without placing any additional demands on the amplifiers.

Dr. Floyd Toole:
When a full-range signal is panned to each of the loudspeakers in turn, and measurements are made at the listening position, we find hugely different bass responses for each of the loudspeakers. The differences are a large as 40dB in this room, and the biggest ones are all at low frequencies. The reason, the woofers each have very different acoustical coupling to the room resonances because they are in different locations. This will be different for every different room. Again, referring back to the circle of confusion the bass that was heard in the control room will not be the same as that heard at home. It cannot be.
Use Identical Subwoofers
As a general rule, if you are using multiple subwoofers, it is best to use identical ones from the same manufacturer. Although using different subwoofers may work, equalization, level matching, and adjustments become much more difficult. In all the research on the use of multiple subwoofers, the experts have used identical subwoofers.

The Science Behind Identical Subwoofers: Assume we have a device with several metallic poles with a bob attached to them. The bobs are colored red, blue, and green. Each pole has a different length, thus having a different natural frequency of vibration. When the red bob is disturbed, it begins vibrating at its natural frequency. This in turn forces the attached bar to vibrate at the same frequency; and this forces the other attached red bob into vibrating at the same natural frequency. This is resonance - one bob vibrating at a given frequency forcing a second object with the same natural frequency into vibrational motion. However, the green and blue bobs would not resonate. This is because the frequency of the red bobs share the same natural frequency. The result is that the second red bob begins vibrating with a huge amplitude. Identical subwoofers will have the same natural frequency and can work together a lot easier to generate smoother low frequency sound.

The following experts recommend using identical subwoofers:

Read Robert Harley's Books. He is the editor of the Absolute Sound Magazine. Robert Harley, Introductory Guide to High-Performance Audio Systems & The Complete Guide to High-End Audio, 558 pages. Also read Richard Hardesty’s articles in Audio Perfectionist.

Polk Audio: Polk Audio - Education, FAQ & Advice, Technology Overviews and Technical White Papers
Using two asymmetrically placed subs will minimize the effects of standing waves in your room, yielding smoother bass response as well as better dynamic range. If using two subwoofers, you must use the identical model of subwoofer. If two different models are used, even from the same manufacturer at some points they will help each other, at others they will fight each other causing a uneven response.
Subwoofer Connection Guide For A Multi Subwoofer System — Reviews and News from Audioholics
We get a lot of questions about what types of subs to purchase for a multiple sub setup. When choosing the right subwoofers for your system, it’s a good idea to choose identical subs for optimal cancellation of room resonances, or ones of similar output level and design. Don’t for example mix and match a high quality 15” servo subwoofer with a cheap dual 6” bandpass sub that came with your “cubed” speaker system. Implementing an inferior subwoofer with a good one will limit your systems dynamic range and bandwidth to the weaker sub making your ears focus on the one that is breaking up and running out of steam. Mixing different subs will also reduce the success of canceling out room resonances since they will exhibit different amplitude and phase responses. Always select two well designed subwoofers (preferably the same) that are each in their own capable of filling your theater room with ample bass without bottoming out or running out of gas. If you can’t afford two subwoofers at the moment, buy one quality sub for now and add a similar capable one down the road when you’ve got the cash.
Two subwoofers are easier to place and result in a flatter frequency response in almost all situations. If you can afford a second matching subwoofer, this is generally preferred to a single more expensive subwoofer. You will almost always achieve a flatter frequency response and a more realistic overall integration with the main system.
In most circumstances two subwoofers will perform better than one. While you might assume this is for added SPL, the greatest benefit will actually be smoother bass response. Two properly positioned subwoofers will distribute the bass throughout the room with greater accuracy than a single sub. If near perfect bass response is your goal, consider using two LFM Series Subwoofers: the Outlaw Audio Scattered Subwoofer Systems.
Wendy Carlos Surround1
In this case I made a trade off for two smaller subwoofers instead of one larger one. With careful A/B comparisons I learned that the bass was nearly the same when the two smaller units were working together as a team as with the single larger unit. But there was, contrary to what I had read, a small amount of additional directionality present with the two subwoofers compared to one.
Sir Terrence, Audio Insider at
The main reason for using identical subwoofers would be identical performance irrespective of room acoustics. With two identical subwoofers, there is a much smaller chance that one will overdrive before the other. If two different size woofers in two different subwoofers are used, the smaller one would have more distortion, more cone motion, and a subtly different sound than the larger one at higher volumes. Even if you use two identical woofers with a different cabinet size, amplifier size, and a different lower frequency limit, one will reach its peak output at a different volume than the other. You want all of your subwoofers to have identical performance to prevent one from dragging another down at high volumes. That is why two identical subwoofers from the same manufacturer are preferred to two different ones.

Forced Vibration
If you were to take a guitar string and stretch it to a given length and a given tightness and pluck it, you would hear a noise that you can barely hear. On the other hand, if the string is attached to the sound box of the guitar, the vibrating string is capable of forcing the sound box into vibrating at that same natural frequency. The sound box in turn forces air particles inside the box into vibration at the same natural frequency as the string. The entire system (string, guitar, and enclosed air) begins vibrating and forces surrounding air particles into vibrational motion. The tendency of one object to force another interconnected object into vibrational motion is referred to as a forced vibration. This causes an increase in the amplitude and thus loudness of the sound. A louder sound is always produced when an accompanying object of greater surface area is forced into vibration at the same natural frequency.

Combining waves
If you are listening to waves from two sources at the same time:
  1. A high pressure from one will cancel out a low pressure from the other.
  2. Two high pressure waves will reinforce each other.
  3. Two low pressure waves will reinforce each other.
When two or more waves with the same frequency reach the ear, the ear interprets these waves as one wave with amplitude as big as the sum or difference of the initial waves. Two sound waves sound good when played together, if one sound has twice the frequency (one octave higher) of the other.

Transient Response
In physics: a short-lived oscillation in a system caused by a sudden change of voltage or current or load.

Transient response: The ability of a component to respond quickly and accurately to changes. Transient response affects reproduction of the attack and decay characteristics of a sound.

Echo and Reverberation
When a wave reaches the boundary, a portion of the wave undergoes reflection and a portion of the wave undergoes transmission across the boundary. Reflection of sound waves off of surfaces can lead to either an echo or a reverberation. A reverberation often occurs in a small room with height, width, and length dimensions of approximately 17 meters or less. Why the 17 meters? The human brain keeps a sound in memory for up to 0.1 seconds. If a reflected sound wave reaches the ear within 0.1 seconds of the initial sound, then it seems that the sound is prolonged. The reception of multiple reflections off of walls and ceilings within 0.1 seconds of each other causes reverberations. Since sound waves travel at about 340 m/s at room temperature, it will take approximately 0.1 seconds for a sound to travel the length of a 17 meter room and back.

Reflection of sound waves also lead to echoes. Echoes are different than reverberations. Echoes occur when a reflected sound wave reaches the ear more than 0.1 seconds after the original sound wave was heard. In this case, the arrival of the second sound wave will be perceived as a second sound rather than the prolonging of the first sound. There will be an echo instead of a reverberation.

Sound & Vision Magazine - Why You Need Four Subwoofers
Sean Olive
ASC Home Theater Acoustics
Acoustics and Vibration Animations
Speed of Sound - Features Archives
ESP - Frequency, Amplitude and dB
Subwoofer Placement For Deep Bass Nirvana
Acoustics Crash Course 1 - Modes
SubwooferSetup and EQ page 2
An Easy Solution To Subwoofer Calibration — Reviews and News from Audioholics
Subwoofer Placement - The Place for Bass Part 1 — Reviews and News from Audioholics
Crawling for Bass - Subwoofer Placement — Reviews and News from Audioholics

Last edited by Big Daddy; 10-08-2012 at 05:41 AM.
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