Speaker Boundary Interference Reflection (SIBR) Calculations

XEagleDriver

XEagleDriver

Audioholic Chief
Gene posted a very interesting video on Speaker Boundary Interference Reflections (SIBR) and how this room/speaker interaction can cause problems different from, but in some ways similar to, the standing wave Room Nodes most of us are more familiar with. Video Link Here.

SIBR Short Course (any errors are mine alone, Gene and his guests, Matt and Anthony did a fine job):
SIBR is the frequency at which a speaker is 1/4 wavelength (distance) away from a boundary wall (e.g. the front and back walls, both side walls, floor and ceiling). At that frequency, the wave reflects back to the speaker from the boundary wall returning to that speaker location at 1/2 wavelength phase (1/4 + 1/4 = 1/2) which is 180 degrees out-of-phase with the original signal and hence causes an amplitude degradation, or even cancellation, at that specific frequency.
Therefore, each speaker has six 1/4 wave SIBR frequencies, one each from reflecting off of: the front wall, back wall, left and right walls, plus floor and ceiling. Some of these SIBR frequencies may not be a problem because some SIBR frequencies are in ranges that speaker is not trying to produce. For example, if a Main speaker is crossed over at 80Hz and happens to have a SIBR frequency at say 45 Hz (well below the 80 Hz x-over) it should not be a problem since that Main speaker is not trying to produce that tone anyway. Same applies for a Subwoofer with a SIBR frequency at say 300 Hz (well above the typical 120 Hz LFE setting).

SIBR Calculator: Their excellent discussion prompted me to develop a SIBR Calculator to calculate the expected SIBR problematic frequencies for the front stage in my HT (two subs & LCR).
I started by listing each speaker and its port(s) down the left of the DISTANCE TO BOUNDARY table below. Ports are included, but kept separate, since a speaker's rear port is at a different distance from the front and back walls than the drivers on the speaker front. I then measured the distance (inches) from each speaker front and/or port to the six boundaries listed across the table (many values were calculated to avoid Death by Tape Measure and highlighted in blue).

These distance values are then fed into the CALCULATED SIBR PROBLEM FREQUENCY table below the DISTANCE TO BOUNDARY table.
The formula used to calculate the SIBR frequency is in cell B3 below or SIBR Freq = 1125 feet/sec divided by 4 times the distance to the boundary in feet.
1125 ft/sec is a typical value for the speed of sound. Dividing by four gives you the 1/4 wavelength needed. The two terms with "feet" units in them cancel each other, leaving 1/second or Hz.
In spreadsheet speak a typical cell formula looks like "=1125/(4*(C9/12)) " where the divide by 12 converts inches to feet and "C9" is a referenced cell in the DISTANCE TO BOUNDARY table above.

Conditional Formatting was used to more clearly identify potential SIBR frequency issues from the "who cares" unimportant values.
Subs highlight frequencies below the LFE Freq (i.e. 120 Hz) in purple.
Ports do the same for frequencies below the Port Freq (i.e. 60 Hz) in yellow.
Lastly, Speakers do the same for frequencies above the X-Over Freq (i.e. 80 Hz) in orange.

Shown here
SIBR CALCULATOR.jpg


CONCLUSIONS:
When multiple problematic SIBR frequencies are close in value for a particular speaker it is more likely to cause bigger problems. For example, the Center speaker has a Front Wall SIBR Freq at 105 and a Floor SIBR Freq at 96 Hz, these two may overlap and reinforce the null in that part of the frequency spectrum. Similarly, the R Main speaker has close SIBR Freq values for the R Wall and Floor.

Looking at this table I would expect potential nulls as follows:
a) Left Sub around 46 Hz (Left Wall for both sub & port), and at 36-39 Hz (Floor & Ceiling)
b) Left Main at 130 Hz (Front Wall)
c) Center 96-105 Hz (Front Wall & Floor)
d) Right Main at 130 Hz (Front Wall) and 84-96 Hz (Right Wall & Floor)
e) Right Sub at 64 Hz (Right Wall for both sub & port)

Although several sub & port cells highlight with 20 to 24 Hz values, these are close to the lower limit of human hearing and have long distances to the boundaries, so I do not expect them to be as audible.

COMPARISON TO ACTUAL MEASUREMENTS:
Four snips below show actual measurements (green line on left side) for the LCR and Subs in that room from a Denon 4500H using the MultiEQ App.
I think these show, to a reasonable degree, some of the nulls expected from the calculations above, particularly for the LCR in the ~84-130 Hz region and the sub in the 50-60 Hz region.

Disclaimer: Matt & Anthony emphasized it is not easy to tell a SIBR Freq problem from a Room Node problem just by looking at a graph. The two may appear the same, cancel or reinforce each other. With in-room measurement, it gets complicated pretty quickly.

MultEQ Front Left.jpg


MultEQ Center.jpg


MultEQ Front Right.jpg


MultEQ Subwoofer.jpg


FINAL CONCLUSION: I obviously need more of a life, and to DRINK more PORT and worry less about speaker ports!!!
 
Last edited:
marticus

marticus

Audioholic
Wow this is a fantastic effort op, I was also intrigued by that video and you're taking it to the next level!
 

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