Help - the effect of inverse square law in open baffle modelling

[timmillea]

I am new to open baffle speakers and I have being delving heavily into the theory of late. To bring myself up to speed I made a spreadsheet just to model the comb filtering on axis as a result of the delayed rear wave arriving with the front wave.

Initially I left out the effect of sound propagation from a point source (a.k.a the inverse square law) because I was not sure if it varied with frequency. When plotted, I obtained the classic open baffle curve (first picture below). This was based on a listening distance of 2m in free space and with a circular baffle of 1m diameter.

Now, the inverse square law applies equally to all frequencies. High frequency loss is attributed to the effect of air absorption which is quoted typically only 0.5dB/100m and so can be safely ignored here.
[http://www.sfu.ca/sonic-studio/handb...pagation.html]

When I add in the effect of the inverse square law, i.e. the rear wave being weaker by a factor of (2/2.5)^2 = 0.64 because it has travelled 2.5m instead of 2m, the graph changes drastically (second picture - same parameters, same scale).

What have I got wrong?

Tim.

[Rudolf]

Originally Posted by timmillea

When I add in the effect of the inverse square law, i.e. the rear wave being weaker by a factor of (2/2.5)^2 = 0.64 because it has travelled 2.5m instead of 2m, the graph changes drastically (second picture - same parameters, same scale).

What have I got wrong?

A wave of 100 Hz - a wavelength of 3.4 m - doesn't really "travel" along a 0.5 m baffle radius. It still has to be considered mostly as a two-point-source-dipole. Your inverse square law will only apply to wavelength which are significantly shorter than the baffle width. So the left end of your diagram is wrong, the right end too. Middle is ok.

Below is what you should expect. (It's a real pity that you can't use EDGE )

Rudolf

[timmillea]

Mmm. I believe in the laws of physics, at least as an excellent approximation. I think you may let me get away with saying that another way of putting what you wrote it is: at baffle sizes much less than a wavelength the source does not behave like a point source.

It is fascinating that a relatively small attenuation of the rear wave would create such a drastically different summed response. The second of the two graphs was brought about by factoring in less than 4dB of rear wave attenuation! I wonder if more effort should be put in trying to attenuate the rear wave?

Originally Posted by Rudolf

(It's a real pity that you can't use EDGE )

Rudolf

It is. I can't find any Mac equivalent but there are signs of activity in the speaker department of the iOS app store.

Tim.

[Rudolf]

Originally Posted by timmillea

I think you may let me get away with saying that another way of putting what you wrote it is: at baffle sizes much less than a wavelength the source does not behave like a point source.

I thought it was this way: At baffle sizes much less than a wavelength the dipole works along the 6 dB/oct dipole loss slope. That is the best area for a dipole to work on since it conserves the true figure-8.

I wonder if more effort should be put in trying to attenuate the rear wave?

Attenuating the rear wave would change the dipole to a cardioid. It is up to you to decide which pattern you like better. My choice is the dipole-8.