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What is the best way to distribute noise from more than one source (I'm envisioning a system with many), within a dome, with the ground as its primary target, at optimal frequencies and volumes to create maximum vibrations on the ground?

Think, this picture - http://hyperphysics.phy-astr.gsu.edu/hbase/acoustic/imgaco/foc3.gif - but with more than one source.

enter image description here

I'm assuming you would want the dome to be perfectly circular, and have the point at which the dome wall meets the ground at a slight incline (as opposed to vertical) so all the sound stays directed at the ground. Imagine a tennis ball which is cut in half, but was split just before the equator. You take the side that is smaller, and flip it over. Thats what I am imagining. I'm just judging from the above drawing that you would want the sound sources crammed as close as possible in the center of the dome, in as perfect as a circle as you could design it, and maybe directed so that they are all pointed to the center of their own, independent, equally sized areas (the dome being the total area of the surface that the sound is being pointed at). It seems like if you could cram all the sound into a point of singularity and put it at the center of the dome, and then release it somehow - that would be ideal (although that sounds pretty complicated). Not sure about frequencies or volumes.

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  • $\begingroup$ Check your link to the image. Seems dead to me. $\endgroup$ – Brandon Enright Jan 20 '14 at 4:09
  • $\begingroup$ not sure if it wasnt working before, but I just double checked it and it should be working now. $\endgroup$ – ewizard Jan 20 '14 at 4:23
  • $\begingroup$ I've added the image to the text... $\endgroup$ – Luboš Motl Jan 20 '14 at 7:27
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    $\begingroup$ Related: xkcd.com/316 :) $\endgroup$ – ybeltukov Jan 20 '14 at 10:51
  • $\begingroup$ @ybeltukov lol - nice $\endgroup$ – ewizard Jan 20 '14 at 19:15
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Consider a combined system where the roof of the room is a parabolic reflector and a 'superfloor' layer is an acoustical Fresnel lens:

enter image description here

The premise would be to match the focal lengths of both systems, starting with the parabolic enclosure, which focuses sound energy from any point in the room at a single point:

$$f_{parabolic} = \frac{d^2}{16 \ h}$$
Then you could use design guidance given by Chan et al 1995 or Hadimioglu 1993 to determine the ideal properties of the Fresnel lens, which will collimate the energy.

Notably, the step height $h$, of the lens, is dependent on the frequency, $f$, you'd like to transmit:

$$h = \frac{1}{N f (\frac{1}{c_{\ air}} - \frac{1}{c_{\ lens}})}$$

where $c_{\ air}$ is the speed of sound in the room,

$c_{\ lens}$ is the speed of sound in the lens material, and

$N$ is the number of phase levels (i.e., how closely to approximates a spherical lens)


I'm not sure how efficient these mechanical devices are, so it may be that there is actually more energy lost in the process than actually reaches the 'subfloor'. (Certainly the parabolic reflector only can focus waves that are directed 'upwards'.) It's also worth mentioning that this system would work best for sources distributed away from the surface of the Fresnel lens so that energy is not shadowed.

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