Feel free to ask questions. I'll do my best to answer.

Wednesday, December 29, 2010

A little more into boundary conditions

The Front wall, side ipsilateral wall, and floor will all cause big issues with your frequency response that will be audible d/t the ear's increased integration time as frequency goes lower.  In other words, we don't hear with the greatest time resolution at low frequencies so we'll hear the reflections as part of the source.  This is why I like wavelets--but that's been touched on earlier in the DTM Blog.  The contralateral wall, ceiling, and possibly even the rear wall will also come into play and more so in a small room I imagine.  As the distance of the reflecting surface gets further away from the source, the less pronounced the dip will be thanks to the Inverse Square Law--every time you double the distance, you loose 6dB.  The manner that the side wall reflections effect what we hear is different than they measure--it's more of spatial distortion and it's been shown to be more enveloping/spacious/and broadens the apparent source width.  These qualities have been shown by Dr. Toole and Mr. Klippel to be preferred vs. their absence.

The equation for the front wall interference:
Cancellation notch frequency = [(344m/s) divided by (4 times the distance from the speaker to the wall behind it in meters)]   (344m/s)/4Dm=fHz
picture for reference:
A quick Table for reference:

This equation for other significant boundaries:
notch frequency = [(344m/s) / 2(the distance of speaker to the listening position via the reflecting surface - the direct path distance from the speaker to the listening position)]   (344m/s)/2(Drm-Ddm)

This picture may help with visualization:
floor bounce
A couple more quick reference tables for this SBIR modifier:
For an online calculator (metric) go here:  
For sidewall reflections:

So for a practical example:
     We have our speaker on a 3 foot stand.  Its Baffle is 4 feet from the front wall and we are sitting we are sitting 9 feet from it at a listening height of 3 feet.  That gives us enough information to find 2 of our first notches.  The front wall will cause an approximate 70 Hz notch while the floor bounce will be a little over 300Hz.  Keep in mind that the ipsilateral wall will still have its say as will the modes and to a lesser degree the other boundaries.  For the ipsilateral problem it will be necessary to go to mehlau.net for a decent calculation.
The previous section was just the the start of
Comb Filtering
The comb filter starts at that first notch frequency related to the SBIR.  If you double that frequency, the interference pattern from the reflected wave is actually additive due to its phase relationship with the original wave.  It is now back in phase and thus you essentially have 2 sources reinforcing each other.  That gives us 6 dB of gain.  This kicks off a pattern of alternation cancellation and reinforcement for multiples of the original notch resembles the teeth of those cheap black plastic combs you all have with the teeth getting progressively closer together as frequency get higher.   It will also become less pronounced with increased frequency d/t narrowing directivity in the MR/Treble. 

Here's the expanded tables from the first section on the effects:
Floor Bounce


  1. Thanks to being self-untaught I had no idea about the inverse square law. Thanks!