Source location relative to room modes

AudioExplorations

New Member
Apr 5, 2012
653
5
0
On his site, Daniel A. Russell, Ph.D. illustrates how room modes are excited as the source location moves across the length of a room (simplified 1D). The key illustrations are the following which illustrate how the first three modes behave in a 5 meter room as the source (red dot) moves across the room (modes at 34.3Hz, 68.6Hz and 102.9Hz shown below).



The first question I have is what is the optimal location of a source in relation to the modes at the modal frequencies? Obviously it will be different for each mode, but am I right in saying that the ideal location is so that the pressure at where ever the listening location may be is as close to 1 as possible? I assume that as the graph drops below zero is the acoustic pressure equal but in opposite phase which would also be an acceptable location as long as it gets you close to -1?

Here are the first 4 modes layered on top of each other, would we want to be as close to the 0.5 point (in this case) at the listening position for as many modes as possible?



So, impossible to find a single speaker/listener location that is optimal for all above modes, and this is not even taking the Y and Z axis into account, let alone the oblique and tangential modes. Of course with using two speakers some of the modes will cancel out given the speakers are in locations of opposite phase of the modes. Now, in rectangular rooms the modal pattern that will exist will have the basically the same shape however differ in frequency depending on the room dimensions.

I am wondering for rectangular rooms if there cannot be a few 'rule of thumb' speaker/listener positioning options that minimise the most problematic axial modes the most and tend to be 'as good as your gonna get' options for positioning? I am sure something like this is possible but there seems to be no such guidance available anywhere. I have compiled a list of speaker placement methods but they all seem to be overly simplified and some cases completely meaningless when trying to optimise modal excitation.

  • Cardas Golden Rule Method - based only on back wall dimension (speaker to side wall = 0.276 x back wall length and speaker to back wall = 0.447 back wall length)
  • Ethan Winer – The ‘38% rule’ - mathematical relationship between speaker (bass driver) and the width and length of the room.
  • Room Mode Calculator - Distance of bass driver from side walls = width / 1.618^4 or width / 1.618^3, bass driver from back wall = length / 1.618^4 or length / 1.618^3.
  • Nordost Method 1 – ‘Audio Arithmetic” Positioning relationship of Y^2 = X*Z where X,Y, and Z are the distances to the nearest boundaries
  • Nordost Method 2 – “Voicing the Room” Based on Wilson Audio method. Subjective listening with the ear, the method aims to optimise for room gain/boundary reinforcement only, nothing to do with room mode positional optimisation.
  • TAS System Set Up Guide

Appreciate if any acoustics experts are able to help me out with this.
 
Last edited:

Nyal Mellor

Industry Expert
Jul 14, 2010
590
4
330
SF Bay Area, CA, USA
On his site, Daniel A. Russell, Ph.D. illustrates how room modes are excited as the source location moves across the length of a room (simplified 1D). The key illustrations are the following which illustrate how the first three modes behave in a 5 meter room as the source (red dot) moves across the room (modes at 34.3Hz, 68.6Hz and 102.9Hz shown below).



The first question I have is what is the optimal location of a source in relation to the modes at the modal frequencies? Obviously it will be different for each mode, but am I right in saying that the ideal location is so that the pressure at where ever the listening location may be is as close to 1 as possible? I assume that as the graph drops below zero is the acoustic pressure equal but in opposite phase which would also be an acceptable location as long as it gets you close to -1?

Here are the first 4 modes layered on top of each other, would we want to be as close to the 0.5 point (in this case) at the listening position for as many modes as possible?



So, impossible to find a single speaker/listener location that is optimal for all above modes, and this is not even taking the Y and Z axis into account, let alone the oblique and tangential modes. Of course with using two speakers some of the modes will cancel out given the speakers are in locations of opposite phase of the modes. Now, in rectangular rooms the modal pattern that will exist will have the basically the same shape however differ in frequency depending on the room dimensions.

I am wondering for rectangular rooms if there cannot be a few 'rule of thumb' speaker/listener positioning options that minimise the most problematic axial modes the most and tend to be 'as good as your gonna get' options for positioning? I am sure something like this is possible but there seems to be no such guidance available anywhere. I have compiled a list of speaker placement methods but they all seem to be overly simplified and some cases completely meaningless when trying to optimise modal excitation.

  • Cardas Golden Rule Method - based only on back wall dimension (speaker to side wall = 0.276 x back wall length and speaker to back wall = 0.447 back wall length)
  • Ethan Winer – The ‘38% rule’ - mathematical relationship between speaker (bass driver) and the width and length of the room.
  • Room Mode Calculator - Distance of bass driver from side walls = width / 1.618^4 or width / 1.618^3, bass driver from back wall = length / 1.618^4 or length / 1.618^3.
  • Nordost Method 1 – ‘Audio Arithmetic” Positioning relationship of Y^2 = X*Z where X,Y, and Z are the distances to the nearest boundaries
  • Nordost Method 2 – “Voicing the Room” Based on Wilson Audio method. Subjective listening with the ear, the method aims to optimise for room gain/boundary reinforcement only, nothing to do with room mode positional optimisation.
  • TAS System Set Up Guide

Appreciate if any acoustics experts are able to help me out with this.

Hi, a quick Q, is this a 'real life room' you are trying to analyze (if so could you describe it), or is it more a theoretical discussion?
 

AudioExplorations

New Member
Apr 5, 2012
653
5
0
It is a theoretical question. To boil down the somewhat long winded question: what is the optimal location of source and listener in relation to the room modes? First in relation to a single room mode, and second in context of the entire modal pattern that takes shape in a rectangular listening room. Thanks for any help with this, it is something I have been struggling with for some time now.
 

Ethan Winer

Banned
Jul 8, 2010
1,231
3
0
75
New Milford, CT
what is the optimal location of source and listener in relation to the room modes? First in relation to a single room mode, and second in context of the entire modal pattern that takes shape in a rectangular listening room.

When considering all modes, which you should for a real-life situation, I have to vote for the 38 percent "rule." But understand that walls and ceilings are not infinitely massive, which adds some absorption and also causes the mode frequencies to shift. Therefore, the best way to optimize placements is to measure the LF response at high resolution as you experiment. Also, even when placements are optimized, the modes still resonate and you still have peaks and nulls. So bass trapping is always needed.

--Ethan
 

Nyal Mellor

Industry Expert
Jul 14, 2010
590
4
330
SF Bay Area, CA, USA
Well my approach is only to worry about the main axial modes up to the 4th ones. They are the ones with the most power, are quite widely spaced (therefore creating peaks with dips between them) and influence what we hear most negatively. The ones that really cause the most issues are in my experience the 2nd and 3rd axial modes. I find locations that work for speaker / listener relative to these modes then use bass trapping to deal with the 100-300Hz range.

For new rooms or odd shaped rooms you either have to make a boundary element model or do what Ethan suggests and find the optimal position through iterative measurements. For rectangular rooms you can pretty much be within 1ft or so by working off a simple room mode calculator that tells you spatially where the peaks and dips are.
 

Jeff Hedback

[Industry Expert]
Feb 9, 2011
62
0
0
Indpls, IN
www.HdAcoustics.net
...good stuff. I'll add that I find the 1st and second order tangential modes (1,1,0 01,1 0,1,0 and 2,1,0 1,2,0 0,2,1...etc...) need attention paid to them.

Also (and in strong agreement with Nyal): in the case of longer rectangular rooms (where length is ~ 1.8x the width) that 3rd order Axial mode can be very strong and only unconventional speaker and/or listener locations can offset.
 

AudioExplorations

New Member
Apr 5, 2012
653
5
0
Thanks all for the replies so far. Although they are very helpful, I still wonder about my original question which is really focusing on the source and listener location in relation to the standing waves.

Modes are often illustrated as one of two graphs, instantaneous pressure (sine wave type graphs where the pressure goes -ve) and instantaneous level (dB) where only the volume is displayed. What I am assuming is that loudspeaker and listener should be positioned such that, for the instantaneous pressure graph, at the listening location the pressure is as close to the 0.75 and 0.25 point (on the Y axis) and on the instantaneous level graph the level is as close to the 0.5 point as possible.

Is this a correct? I guess this would put you in a position where you are neither in a peak or a null.

What I have done to try to answer this question myself is work out what the various guidelines recommend.

Ethan's 38% rule = 38% point (this seems to be focusing mainly on the first axial mode however for the 2nd and 3rd mode puts you fairly close to the peaks, good position for the 4th)
Cardas Golden Rule Method = At the 27.6% point (pretty good for the first and second axis modes, and near peaks for the 3rd and 4th)
Room Mode Calculator - width / 1.618^4 (14.6%) or width / 1.618^3 (23.6%), (14.6% puts you near peak of the first axial mode, great position for the 2, 3, and 4th modes, 23.6% seems to find an ideal place for the 1-3 modes but pretty much in the peak for the 4th mode).

comparison.jpg

Am I looking at this right?
 

Jeff Hedback

[Industry Expert]
Feb 9, 2011
62
0
0
Indpls, IN
www.HdAcoustics.net
Yes AudioExplorations that is the right method to view and use modal predictive tools. A minor point that to me helps understand things even greater is that modes are not instantaneous. In fact, it takes somewhere between say 45ms and 65ms for the modes to begin to resonate (frequency and room dependent) and another couple hundred milliseconds to see how fully resonant they really are.

If the room has "good/favorable" dimensions then I do try to locate the speakers and ears in a place where you're exciting "all modes some" but not "some modes all". If your room has modal issues due to dimensions, then you can use your very same method to place spkr/listeners to reduce that problem (like the example I offered above with the longer rectangular room and the 3rd axial mode).
 

Ethan Winer

Banned
Jul 8, 2010
1,231
3
0
75
New Milford, CT
You're in good hands with Jeff and Nyal, but I can address this:

Modes are often illustrated as one of two graphs, instantaneous pressure (sine wave type graphs where the pressure goes -ve) and instantaneous level (dB) where only the volume is displayed.

In fact these are the same thing. Greater pressure creates louder volume because our ears respond to pressure.

--Ethan
 

AudioExplorations

New Member
Apr 5, 2012
653
5
0
Yes, just that with the level the +ve and -ve phase is not taken into account... but these are to our ears perceived the same.

Ethan, can you expand a little bit on your reasoning behind the 38% and why you consider this to be the best location within the modal pattern? Are you considering just axial modes across a single axis or does it also take into account the Y axis and perhaps any tangential or oblique modes?
 

Rutgar

New Member
Apr 20, 2010
212
2
0
Dallas Area
mysite.verizon.net
The 38 percent "rule" was first proposed by studio designer Wes Lachot. It averages the response for the first six multiples of the axial length mode. More about it in the sidebar of this article:

How to set up a room

--Ethan

Interesting. For grins, I decided to see where things fall in my room using the '38% rule'. My listening position is about 9 inches closer to the back wall than where this rule would put it. But, my speakers (front center) are practically dead on, the 38% mark from my front wall (which I positioned just using my ear).
 

About us

  • What’s Best Forum is THE forum for high end audio, product reviews, advice and sharing experiences on the best of everything else. This is THE place where audiophiles and audio companies discuss vintage, contemporary and new audio products, music servers, music streamers, computer audio, digital-to-analog converters, turntables, phono stages, cartridges, reel-to-reel tape machines, speakers, headphones and tube and solid-state amplification. Founded in 2010 What’s Best Forum invites intelligent and courteous people of all interests and backgrounds to describe and discuss the best of everything. From beginners to life-long hobbyists to industry professionals, we enjoy learning about new things and meeting new people, and participating in spirited debates.

Quick Navigation

User Menu

Steve Williams
Site Founder | Site Owner | Administrator
Ron Resnick
Site Co-Owner | Administrator
Julian (The Fixer)
Website Build | Marketing Managersing