I am training an animal (let's assume it's a rat) to do sound-source localization in a cylindrical plexiglass chamber that is approximately 30 cm in diameter (see figure). That is, the animal must approach the speaker that is presently on (there are four speakers present, one is on, the other three are off). Sound is 70dB at 10kHz.

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They are getting confused, perhaps due to echoes or reverberations in the chamber. I am not sure how to optimally design the chamber (i.e., frequency and volume of sound source, and diameter of cylinder) to minimize confusion.

In case this is a known problem from partial differential equations, the cylinder is closed on the floor, open on the top and we can consider the speaker a point source for all intents and purposes (it is a piezo buzzer with a pure tone).

We have argued about whether sound should be extra loud to help them find the right source, or perhaps quiet to minimize echo/reverb in the chamber. Ultimately I think there is an optimum value to minimize all these effects. I have cracked open my Giancoli Freshman Physics book but it didn't get beyond unencumbered sound travel, and the basics of wave reflection (e.g., angle of reflection = angle of incidence: e.g., what you'd find at Wikipedia - https://en.wikipedia.org/wiki/Reflection_%28physics%29).

Adding a padded inner surface to dampen reflection is not an option because the animals will climb it and escape to freedom.

Their errors seem fairly random. For instance, when the speaker turns on to the right they go to the left instead. I know they can do these types of tasks in general: when I replace speakers with little LED lights, they learn it in a couple of days and they are very happy. I really think this is a problem with the acoustical physics of my setup.

[If someone were to suggest a simple piece of software to model sound in simple reflective enclosures I would not complain about it--I searched and didn't find it--but I am not asking for such a tool because I know this question would get closed for asking such an off-topic question about tools :)]

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    $\begingroup$ Well.... this is actually a known problem from partial differential equations. In particular the Helmhltz Equation. Thus, for your tool (the simple piece of software to model sound), anything that solves this equation numerically, will do. $\endgroup$ – Physicist137 Jul 23 '16 at 16:36

Loudness will not help. You do indeed have a (big) problem with reflection - the geometry is really designed to make the poor rat's task impossible.

You need to manage the reflections. Since you state that modifying the surface is not an option, I would recommend tapering the walls - instead of being vertical, you might place them at a 15 degree angle (steep enough that the rat can't climb out - anyway I assume you can place a mesh over the top.) This will ensure that the echo will be aimed "up" rather than sideways.

Here is a simple construction to show you what is happening:

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The source (at S) creates constructive interference at E. By sloping the walls you can make E happen above the level of the rat's ears - it will make the task much more manageable.

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From this diagram you can see that making the diameter larger allows steeper slopes.

Incidentally - the fact that curved surfaces have the property of focusing sound has been known for many centuries. There is this pulpit in a Philadephia church (church of the Gesu):

enter image description here

(Image source - Baillinger collection)

Similar structures have been used in churches and theaters - the Mormon Tabernacle in Salt Lake City, the Pantheon in Rome, and the many semicircular theaters and their alcoves used to reflect sound, all employ this principle. And now you have to defeat it...

Unfortunately, making the diameter larger but leaving the walls vertical will basically do nothing to improve the situation - the focusing effect of the walls means that the sound will be very effectively focused, regardless of the diameter. This is why you can hear a whisper from across the Pantheon...

  • $\begingroup$ Very clever design. Basically, given the present design, we should maximize the diameter to minimize these effects. Or, minimize the volume (minimizing volume is similar to maximizing diameter). So basically loud enough to hear easily, but no louder. At which point this isn't really a physics question....but one of sensory thresholds. But you have confirmed what I feared: we have basically developed a chamber that makes this task really, really hard. $\endgroup$ – neuronet Jul 23 '16 at 16:54
  • $\begingroup$ So in response to your recent edit, my last comment was wrong...increasing diameter is actuallyl sort of useless...Crap. I will change the frequency of sound in each location so they aren't all identical. Unfortunately putting a mesh over the top isn't possible there is cabling going in and out..for the neuronal recordings! :) $\endgroup$ – neuronet Jul 27 '16 at 15:22
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    $\begingroup$ Perhaps you can add some sound absorbing materials up to a certain height only, and leave the upper part of the walls smooth. That would eliminate a lot of the echos but keep the escape artists in the test arena. $\endgroup$ – Floris Jul 27 '16 at 16:18
  • $\begingroup$ Yes that is a good idea, pretty much anything would be better than acrylic. Ultimately I think we need to redesign the chamber, sigh. :) Also I'm calculating acoustic resonance frequencies in the chamber (based on diameter, height of cylinder) and making sure we avoid resonance frequencies in our tone. $\endgroup$ – neuronet Jul 30 '16 at 16:13

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