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Using subwoofers to improve sound quality: Part 1 – Speaker Boundary Interference

An introduction to speaker boundary interference

Deep nulls in the frequency response in the bass region can be caused by phase cancellation between the direct sound wave from a sound producing device and the indirect sound wave that has reflected from a nearby boundary such as the floor, ceiling or walls. This phenomenon is called speaker boundary interference or SBIR for short. This measurement shows an example of SBIR effects:

The frequency of the SBIR dip changes according to distance from the boundary according to the formula:

Frequency of cancellation = speed of sound / (2 x path length difference)

This relationship between cancellation frequency and path length difference can be exploited to remove SBIR effects.

How using a subwoofer can reduce speaker boundary inteference

A simplified example and picture will help illustrate both SBIR and how using a subwoofer can reduce its effects.

Take the common situation of a speaker which is placed 4ft out from the back wall as in the diagram. Using the formula introduced above we can calculate a cancellation at 71Hz due to a path length difference between the direct and indirect sound of 8ft. Now a sub is introduced into the system and a crossover point of 80Hz selected. The sub is placed 1ft from the back wall. Calculating the theoretical cancellation frequency for the sub, we see that this is at 141 282Hz. Since the sub is crossed over at 80Hz there is only limited cancellation at 141 282Hz since the frequency response is many dB down as a result of the rolloff of frequencies above the crossover point. The cancellation caused by the main speakers being 4ft out from the back wall is also reduced since the crossover is attenuating frequencies below the crossover point.

What do you think about this cunning subwoofery?

17 thoughts on “Using subwoofers to improve sound quality: Part 1 – Speaker Boundary Interference”

  1. Is the math correct? Based on your eg with listener 15 ft fr back wall. Subwoofer 1 ft from the back wall. Indirect path distance 16 ft. Direct path 14 ft, so cancellation freq, 1130/ 2x 2 = 282 hz

  2. Hi Audioblazer – wow you are quite right…not sure how I missed that…thanks!

    For readers – I have updated the article to reflect the correct cancellation frequency of 282Hz.

  3. Hey Nyal.

    I currently am trying to decide which bookshelf speaker stand height to buy. The 36 inch stand will get my pioneer Andrew Jones bs22’s 3 ft. off the floor and allow me to set my subs’ crossovers to 100 to negate SBIR. However, that would put my tweeter 6 inches above my ears. If I buy the 30 inch stand my tweeter will be at ear height, but I will most certainly have some suckout as I have hardwood floors and the only absorption would be a thick area rug.

    You have been doing this for a while. Which would consider doing?

    Thank you for your great website and informative write ups. I always refer people to read your blogs. Have a good one.


    1. Hi John

      Thanks for reading. I don’t quite get your strategy of avoiding SBIR through using a 36″ height stand. I’m guessing you are referring to either the floor or ceiling bounce SBIR? For either the path length difference with a 30″ vs 36″ is going to be negligible. Reflected path length for either is a path from the speaker’s acoustical center to the floor between the listening position and the speaker and then back up to your ears.



      1. Thanks for the quick reply, Nyal.

        I was under the impression that ceilings and floors would cause SBIR just as much as the side walls. I had calculated SBIR suckout at 94 hz if I positioned my speakers 3 ft from each boundary ( which I assumed meant ceilings and floors as well) I then could effectively rid my room from the suckout at 94 hz by positioning my subs in the corners and setting the crossover to 100 Hz.

        Thanks for your time. Am I understanding this correctly?

        1. Yes ceiling and floors also cause SBIR, but just make sure when you are calculating SBIR frequencies that you are looking at the path length difference between the direct and reflected sound, NOT the distance of the speakers from a boundary. The path length difference for a ceiling reflection you can calculate via a CAD model, some trigonometry or using string. The reflected path length is distance from the speaker to the ceiling first reflection point (as you would find it if you used the ‘mirror trick’) plus the distance from the ceiling first reflection point to the listener. The direct path length is a straight line from the speaker to the listener.

  4. Hi Nyal,
    Great website!
    I’m about to explore three subwoofer changes in my control room to eek out a few more db of an improved response. My goals are entirely oriented toward flat response at the mix position. I’m aware of the changes at other locations but they don’t impact my work. I have and use Fuzzmeasure and have access to Smaart as well. My room has a vaulted ceiling so normal measurement for room modes fall short. The peak runs from front to back, so I am Symetrical left to right.

    1. I’m going to try to time align my subs both via location and electronically. Any tools or recommended procedures?
    2. I will Bump from two front subs to four( two front and two rear ). I read about reversing the phase on the rears. Do you do this or do you measure the phase and adjust it? If so how?
    3. Adjust the height of the subwoofers. Any thought about that process?
    Thanks and sorry for the deep questions….. 🙂

    1. Hi Dan

      Thanks for your message.

      Basic sub alignment theory is that you adjust for maximum SPL at the crossover frequency using the phase and polarity controls on the sub. This is quite easy to do, as you only have to look at the frequency response graph and only have a few controls to adjust. Although not directly addressing your situation, our blog article on sub integration for stereo systems will point you in the right direction.

      This technique doesn’t necessarily result in the best possible integration. For that you have to use more sophisticated techniques, including looking at the phase and impulse response graphs to adjust the time delay for the speaker and each sub. The basic tools you need are a measurement system with phase and impulse response views, which you have, and a digital crossover with sufficient time delay to align everything. I’d recommend the Xilica XP series of DSP processors here, probably the XP4080. There are also other tools you could use, depending on how many independent sub channels you need control over. Unfortunately I haven’t written a process on how to integrate multi-subs or use these more advanced processors. It is on the list but not sure I’ll get to it anytime soon. You and all the other blog readers should know we can do sub integration work remotely; we dial into your computer to control both the measurement system and DSP.

      With respect to your question on reversed phase on the rear subs, really that is just another way of time aligning them. Phase, polarity and time delay are all doing similar things. Finally, for sub height, that only makes a real difference if you can position your subs in a positive polarity of some height modes and other subs in the negative polarity (which is covered in this blog article).

  5. As much I I think I know about audio, I am really struggling to understand this article. Feels like you need to be a rocket scientist. Let’s put aside the technical mumbo jumbo for a minute and go back to basics. How does the subwoofer reduce SBIR when it will be placed in the corner? It’s got walls which will be reflecting… As en example If I have 2 subs in the far right and left corner of my room on the front wall beside the speakers and crossover is at 80hz, while the speaker is 17cm of the front wall(small speakers) is my SBIR going to be better than without the subs and speakers running at full range?

    1. It’s to do with the frequency at which the SBIR occurs. If you put a sound source closer to a boundary then the SBIR frequency is increased, if you put it further away then the SBIR frequency is lowered. If you put your speakers so the SBIR frequency is below the crossover point to the sub, and put the sub so the SBIR frequency is above the crossover point to the speaker, then you have reduced SBIR through use of the subwoofer and crossing over the mains to it. Obviously the crossover is not a “brick wall” (infinite slope filter), so depending on where you place the speakers and subs, you may still see a little SBIR.

  6. Hi,
    Just read this, and i’m intrigued. Some doubts:

    1- Isn’t the situation plotted very theorethical, with a lot of ifs?:
    a) if the speakers are bipolar, for the back radiation to be exactly the same as front one, otherwise, the speaker box would retard and weaken the signals reflected by the back wall, making the calculation invalid;
    b) if the backwall is a perfect mirror of the frecuency calculated (truly difficult, I understand);
    c) if there are no spur omnidirectional refractions in the back wall (also difficult);
    d) if there are no other delays from the other adjacent walls, which in theory is impossible unless those walls are completely inhert, or you are in free space;
    e) given that the bass region is completely omnidirectional, there should be multiple boosts and cancellations coming from all walls, and several frecuencies. Wouldn’t the only way to discard cancellations be to have a much stronger direct signal in relation to the indirect reflections coming from the room?

    2) Even if you fix one given frecuency with a SW, wouldn’t you have similar problems with multiple other frecuencies? Wouldn’t every emiting source be inducing cancellations from most walls at some frecuencies? What you fix at one frecuency wouldn´t mean new cancellations (or resonances) at other frecuencies?

    1. Hi Pablo, much of what you say is of course correct.

      A) if the speakers were bipolar (in phase rearward radiation) then of course you would have some phase shift between front and rear sources depending on the distance between them on the speaker cabinet. That phase shift would cause some cancellations in the frequency domain but they’d likely be higher up in the operating range than where you would cross over to subwoofers, since the distance between the two drivers would likely be small relative to the wavelengths we are talking about.
      B) sure, the back wall will have some absorption which will reduce the strength of the back wave
      C) not sure what you mean by ‘spur omnidirectional refraction’, can’t say I’ve come across that term before?
      D) of course, a single boundary is a simplification
      E) if you position the speakers either very close to boundaries (see Allison’s published AES papers on the subject), or far enough away the SBIR null is above the sub operating range, then you can mostly avoid the issue. It’s the middle ground that’s dangerous

      2) yes on your first point here, see Allison. Adding subs against walls doesn’t tend to cause new issues

  7. I understand that this example is simplified to explain the basic principals. But in reality, that speaker & its output is a four dimensional object in a four dimensional space. There are alot more reflections than discussed, as others have brought up. I understand that adding subwoofers is the point to the exercise, but my experience is that most audio purists do not want the complexity (adding time, phase and equipment options variability not to mention digital losses) of added subwoofers. It takes careful balancing of the major reflections relative to the listening location for relatively flat response. Add the reflectivity of wall finishes, surfaces & resonant frequecies of systems within the room and the bass can change noticeably. The best answer is having someone who understands the varibles and balances the relative importance of each to suit the listeners taste and hearing.

    1. Hi John, it is our opinion that a good audio system will nearly always sound better with a properly integrated subwoofer system. I’ve only come across maybe 1 or 2 examples in 10 years where the system did not sound drastically better after adding subwoofers. Subwoofers / EQ give you SO much control over the sub-100Hz region, which is most rooms is a complete disaster in terms of neutrality and flatness. Most speakers are no where near flat to 20Hz either.

  8. Hi Nyal, awesome info here.

    So if one was able to do this, then it would negate needing to place an absorption acoustic panel behind the left and right mains to combat SBIR, correct?
    So for me, if my front tower was at 94hz and used a crossover of 100hz to the subs, while the subs frequency was at 129hz I should be good?
    If that is acceptable would it be better to do that or push the front tower closer to the wall so it is at 187hz and use a 3″ absorption panel behind it to manage the SBIR?

    1. Either option works, but note a crossover is not a brick wall, so you will still have some SBIR effects below crossover.

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