Noise abatement for a rack

[Robert G. Brown]

On Wed, 4 Dec 2002, Kegley, Russell B wrote:

> I haven't ever tried this, but what about active noise cancellation?  I'm
> thinking the relatively cheap ($100 or so) headphones, but the idea of
> damping the noise in the whole room is intriguing.   One URL I found that
> I'm going to look into further:
> 
> http://users.erols.com/ruckman/ancfaq.htm

In noise cancellation headphones, the wave path for the sound being
cancelled is very short -- a cm or two -- and the sound being cancelled
can be measured and phase inverted on the way in through the headphones.

Trying to cancel the noise "in the whole room" with something like an
array of wall mounted cancellation units is a mind-bogglingly difficult
problem in wave mechanics to begin with, and (in my opinion) just can't
be made to work without something like defense department resources (the
problem isn't TOO dissimilar to cancellation of e.g.  reflected radar
images, just mind-bogglingly harder).

First of all, it is noise, with little to work with in the way of
coherence length or signal persistence.  Second it is broad spectrum
noise, with frequencies all over the place and with wavelength ranging
from tens of meters (order of the size of the room) to a few centimeters
(order of the size of small features in the room) bouncing and
interfering all over the place.  Finally, it is broad spectrum noise
with wavelengths ranging etc with widely distributed independent
sources.

I imagine that the e.g. pressure wave profile in any plane running
through the room looks something like the surface of an incredibly
choppy sea.  Cancelling the waves propagating into a single local
channel (your ear) is possible because you DON'T need to sample or know
about the waves anywhere but right at the entrance to the channel, and
there you can easily generate a full spectrum of sound at higher
amplitude than the incoming waves.  Cancelling the waves on the ocean
surface itself?  In three dimensions?  With cancellation units "far"
from the sources?

Not impossible, maybe (maybe it is -- have to ask a mathematician and
wait a year or two:-) but at the very least you'd need to sample the
waves all over the room, solve a pretty nasty mathematical problem in
real time, and generate a counterwave from the array of emitters.
Anywhere you fail to achieve cancellation you're likely to get phase
coherent addition and a manifold INCREASE in sound intensity -- sound
"hot spots".

Lo, the website/FAQ above points this out (in less detail:-):

  Controlling a spatially complicated sound field is beyond today's
  technology. The sound field surrounding your house when the neighbor's
  kid plays his electric guitar is hopelessly complex because of the
  high frequencies involved and the complicated geometry of the house
  and its surroundings. On the other hand, it is somewhat easier to
  control noise in an enclosed space such as a vehicle cabin at low
  frequencies where the wavelength is similar to (or longer than) one or
  more of the cabin dimensions. Easier still is controlling
  low-frequency noise in a duct, where two dimensions of the enclosed
  space are small with respect to wavelength. The extreme case would be
  low-frequency noise in a small box, where the enclosed space appears
  small in all directions compared to the acoustic wavelength.

The latter two cases, with control space small in all directions
compared to nearly all the wavelengths being controlled, corresponds to
noise-cancelling headphones, which I'm sure work just fine.  As for the
larger space, well, using the beowulf itself we could probably sample
the sound each nodes is producing very close to the source.  We could
probably install sound cards and drive little minispeakers inside the
chassis that generate cancellation antiwaves in the primary sound
emitting apertures, and maybe even handle resonant acoustical waves
given off by the case surfaces.  By cancelling the waves within
centimeters of the sources we should be able to eliminate most of the
outward going wave, at each node, one node at a time, in embarrassingly
parallel.  That would do it for the nodes I think.  To do the AC system
would be harder -- we'd probably need a few nodes to do that as well,
with distributed sensors and counterwave emitters close to the primary
emission points (and would probably have to wrap the ductwork and so
forth to actively damp it).

To put it another way, cancelling the kids electric guitar wave is easy
-- if you can do it with several speakers "right next to" (surrounding)
the emitting speaker, or better yet, with another speaker right on top
of the emitting speaker.

So, an autonoise-cancellation beowulf.  Might not have a lot of leftover
horsepower (all the computations required would need to be pretty much
in realtime).  However, one could try to prototype this way, create an
ASIC coprocessor for a sound card, and equip the nodes with active noise
cancellation as a "feature", putting a small speaker "on top of" each
fan.  This, in all seriousness, is probably possible and mass
produceable for $100 or so (so cheap because it IS a hack of existing
sound cards, although you'd probably need several independent channels).

Shall we write a grant proposal?  Anybody want to fund a patent?

   rgb

-- 
Robert G. Brown	                       http://www.phy.duke.edu/~rgb/
Duke University Dept. of Physics, Box 90305
Durham, N.C. 27708-0305
Phone: 1-919-660-2567  Fax: 919-660-2525     email:rgb at phy.duke.edu