Distance Attenuation WFS-Renderer

[Mario Herberger]

Dear SSR-Team,

During experiments on the physical properties of the WFS renderer, the following topic came up for me:
Despite setting a decay exponent of 1, the distance attenuation is not at 1/r. The distance attenuation was more at 1/sqrt(r).  Do you know why this could happen?

The scenario was implemented with 8 loudspeakers in distances between 1-8m from the point source. The orientation of the loudspeakers was directly in the other direction to the source, that 100% of the signals could reach the loudspeakers. I put in a .wav-file with a mono-sinus-signal of 440Hz. The amplitude-reference-distance was at default. 

Should you need further information please do not hesitate to contact me!

Thank you in advance for your help!

Best regards,

Mario Herberger

[Jens Ahrens]

Hi Mario,

I can't recall all details (it was 15 years ago that we programmed that part), but my guess is the following:

Let'a differentiate virtual space and real space. The virtual space is the space "behind" the loudspeaker array where the virtual sources are located, and the real space is the space that is bounded by the loudspeaker array and where the listener is located. Any sound field synthesis method incl. WFS can generally only synthesize a sound field with a correct amplitude decay if it employs surfaces of loudspeakers (say, a spherical surface that encloses the listening area, i.e. the "real space"). As this is very impractical because of the massive amount of loudspeakers required, WFS is usually implemented with 1 D loudspeaker arrays (lines, circles, etc). This is what the SSR WFS renderer was made of. This requires fewer loudspeakers, but the price to pay is the circumstance that the amplitude evolution in the real space is not correct. 

To mitigate this, we introduced a "reference point" in SSR, which is the point at which the amplitude of a virtual sound source is correct, no matter where the sound source is. By looking at the positions of the loudspeakers and the virtual sources (i.e. the amplitude decay in the virtual space and the real space), SSR computes a correction of the amplitude such that the resulting sound field has the correct amplitude at the reference point. 

So, I would guess that the amplitude decay that you will observe in your setup will change with the choice of the reference point. Try to set the reference point very close to the loudspeaker of interest (it might not be possible to set it at exactly the same location like the loudspeaker because SSR would need to divide by zero then). 

Best,

Jens

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