Reply by Frnak McKenney●December 22, 20082008-12-22
Hi, Eric. Thanks for joining in.
Our story so far (trimmed... in keeping with the holidays <grin!>)):
On Sun, 21 Dec 2008 09:09:16 -0700, Eric Jacobsen <eric.jacobsen@ieee.org> wrote:
> On Sun, 21 Dec 2008 07:39:42 -0600, Frnak McKenney
><frnak@far.from.the.madding.crowd.com> wrote:
>
>>On Sat, 20 Dec 2008 17:04:16 -0500, Philip Martel <pomartel@comcast.net> wrote:
>>>
>>> "Frnak McKenney" <frnak@far.from.the.madding.crowd.com> wrote in message
>>> news:856dnZH-b6KZjNDUnZ2dnUVZ_vSdnZ2d@earthlink.com...
>>>> On Thu, 18 Dec 2008 17:02:32 -0600, FordPrefect <altermyego42@gmail.com>
>>>> wrote:
>>>>> Hi.. I needed a few tips on 2-D localisation of a sound source using 2
>>>>> microphones (COLLINEAR WITH THE SOURCE). The source is assumed to be a
>>>>> single frequency source and in-accessible with the only known
>>>>> characteristics being the ones measured from an oscilloscope.
--snip--
>>>> Just to make sure we're working with the same impression, I'm
>>>> interpreting your phrase "COLLINEAR WITH THE SOURCE" this way:
>>>>
>>>> S: source
>>>> M1,M2: microphones
>>>>
>>>> A-----M1---------M2---------S-----B
--snip--
>>>> And I'm assuming this is a "mathematical" problem (Oscilloscope has
>>>> infinite bandwidth and values can be read from it with infinite
>>>> precision, microphones are omnidirectional and infinitely small and
>>>> can be placed with infinite accuracy, instantaneous measurements,
>>>> etc.)
>>>>
>>>> S is a "single-frequency source" -- a simple sine wave with
>>>> frequency "F". You can measure F with the 'scope, which, with the
>>>> speed of sound in air will yield wavelength -- the length of one
>>>> full compression-rarefaction cycle from S.
--snip--
And I now wish I hadn't said:
>>>> ...it's insoluble, at least as stated. You need
>>>> more information, such as "the position of S is known within a
>>>> one-wavelength distance", or "S starts and stops", or something
>>>> else.
--snip--
And Philip contributed the Something Else:
>>> Well, the intensity of a sound falls off as 1/(distance^2).
-- embarassingly obvious math snipped <grin!> --
I tried to cover my assets with:
>>There's still a bit of ambiguity in that, given S is a point source,
>>and it's also presumably invisible and in another room so you can't
>>"see" it or "listen" to it, you could be dealing with:
>>
>> A----M2-------------M1-------S--------B
>>
>>or
>>
>> A----M2----------------------S--------M1-------B
--snip--
> Using the power decay works great when there are no reflections, but
> often works very poorly for the cases like you described where the
> sensors and emitter may be in a room or different rooms (or when
> there's interference).
I'm not sure I stated all my assumptions, but the mental image
I was working with had S, M1, and M2 in a separate location, one
isoalted from O, the unnamed-in-this-context Observer with his
trusty Oscilloscope. S's position within that location was unknown,
but I did assume that the positions of M1 and M2 were known to any
required degree of accuracy and could be repositioned anywhere with
equal accuracy (waldoes? elves?). And since the original problem
statement didn't mention the possibility of interference, I ignored
it as well (not something I'd feel safe doing in the RealWorld(tm)
<grin!>).
> If the signal really is just a tone, it's going to be a tough nut to
> crack without some significant limiting assumptions.
When you're working with a textbook problem (or something equally
realistic, say as an astral projection <grin!>) one can get away with
a lot of assumptions that wouldn't be reasonable to make when one is
working on a customer's problem. If nothing else, the consequences of
errors are generally much less severe: a couple of exam points vs.
the possible loss of a contract. <grin!>
Meanwhile, the OP appears to have folded his tent and stolen off into
the night, leaving behind only speculation. Sigh.
Frank
--
There is something fascinating about science. One gets such
wholesome returns of conjectures out of such trifing
investment of fact. -- Mark Twain
--
Frank McKenney, McKenney Associates
Richmond, Virginia / (804) 320-4887
Munged E-mail: frank uscore mckenney ayut mined spring dawt cahm (y'all)
Reply by Eric Jacobsen●December 21, 20082008-12-21
On Sun, 21 Dec 2008 07:39:42 -0600, Frnak McKenney
<frnak@far.from.the.madding.crowd.com> wrote:
>On Sat, 20 Dec 2008 17:04:16 -0500, Philip Martel <pomartel@comcast.net> wrote:
>>
>> "Frnak McKenney" <frnak@far.from.the.madding.crowd.com> wrote in message
>> news:856dnZH-b6KZjNDUnZ2dnUVZ_vSdnZ2d@earthlink.com...
>>> On Thu, 18 Dec 2008 17:02:32 -0600, FordPrefect <altermyego42@gmail.com>
>>> wrote:
>>>> Hi.. I needed a few tips on 2-D localisation of a sound source using 2
>>>> microphones (COLLINEAR WITH THE SOURCE). The source is assumed to be a
>>>> single frequency source and in-accessible with the only known
>>>> characteristics being the ones measured from an oscilloscope.
>>>> Oh, and I'm a Mechanical Engineer with ABSOLUTELY NO PRIOR EXPOSURE TO
>>>> DSP
>>>> so please be kind enough to elaborate those "few tips"...Thanks :-)
>>>
>>> Ford,
>>>
>>> Just to make sure we're working with the same impression, I'm
>>> interpreting your phrase "COLLINEAR WITH THE SOURCE" this way:
>>>
>>> S: source
>>> M1,M2: microphones
>>>
>>> A-----M1---------M2---------S-----B
>>>
>>> As Fred has pointed out, as stated this is a 1-D localization
>>> problem, not a 2-D problem.
>>>
>>> And I'm assuming this is a "mathematical" problem (Oscilloscope has
>>> infinite bandwidth and values can be read from it with infinite
>>> precision, microphones are omnidirectional and infinitely small and
>>> can be placed with infinite accuracy, instantaneous measurements,
>>> etc.)
>>>
>>> S is a "single-frequency source" -- a simple sine wave with
>>> frequency "F". You can measure F with the 'scope, which, with the
>>> speed of sound in air will yield wavelength -- the length of one
>>> full compression-rarefaction cycle from S.
>>>
>>> But... unless you have some way of causing a recognizable "hiccup"
>>> from S -- starting and stopping it, for example -- I think I have to
>>> go along with Fred: it's insoluble, at least as stated. You need
>>> more information, such as "the position of S is known within a
>>> one-wavelength distance", or "S starts and stops", or something
>>> else.
>>>
>> Well, the intensity of a sound falls off as 1/(distance^2). Assuming that
>> both microphones are on the same side of the sound source, let the amplitude
>> of the sound as measured at the mics be A1 and A2 and the distance between
>> the source and the mics be d1 and d2. Let the distance between the mics be
>> d, and to simplify the math let A1 >A2 (and therefore d1 < d2). Call the
>> amplitude of the sound at unit distance A.
>> A1 = A/(d1^2)
>> A2 = A/(d2^2) = (A/((d1+d)^2)
>> so A1/A2 = (d1+d)^2/d1^2)
>> (d1+d)/d1 = sqrt(A1/A2) = R
>> d1+d = R* d1
>> d = (R-1)* d1
>> d1 = d/(R-1) = d(sqrt(A1/A2)-1)
>
>Philip,
>
>Well color me purple and call me an eggplant!
>
>I was really enjoying these nice trees... where did this _forest_
>suddenly appear from? <grin?>
>
>There's still a bit of ambiguity in that, given S is a point source,
>and it's also presumably invisible and in another room so you can't
>"see" it or "listen" to it, you could be dealing with:
>
>
> A----M2-------------M1-------S--------B
>
>or
>
> A----M2----------------------S--------M1-------B
>
>but you do know that S is to the "right" of the microphone with the
>weaker signal. Taking a third reading off to the "left" of _that_
>microphone guarantees that you can combine its amplitude and the
>amplitude measured at the microphone with the weaker signal, using
>your forumlation, and trust the result.
>
>This could explain why collinearity was introduced, although the
>"amplitude" approach could equally handle a 2-D or 3-D location
>problem. You'd just need to take more measurements.
>
>I think I'll go fix another cup of tea (hopefully the results will
>be slightly less embarassing <grin!>). Anyone see a way to solve
>this with only two measurements?
>
>Thanks, Philip.
>
>
>Frank
>--
> "Science is not a linear march to truth but a tortuous road with
> blind alleys and a rubbernecking delay every mile or two. Our
> road map is not objective reality but the patterns of human
> thoughts and theories."
> -- Stephen Jay Gould, "Eight Little Piggies"
Using the power decay works great when there are no reflections, but
often works very poorly for the cases like you described where the
sensors and emitter may be in a room or different rooms (or when
there's interference).
If the signal really is just a tone, it's going to be a tough nut to
crack without some significant limiting assumptions.
Eric Jacobsen
Minister of Algorithms
Abineau Communications
http://www.ericjacobsen.org
Blog: http://www.dsprelated.com/blogs-1/hf/Eric_Jacobsen.php
Reply by Frnak McKenney●December 21, 20082008-12-21
On Sat, 20 Dec 2008 17:04:16 -0500, Philip Martel <pomartel@comcast.net> wrote:
>
> "Frnak McKenney" <frnak@far.from.the.madding.crowd.com> wrote in message
> news:856dnZH-b6KZjNDUnZ2dnUVZ_vSdnZ2d@earthlink.com...
>> On Thu, 18 Dec 2008 17:02:32 -0600, FordPrefect <altermyego42@gmail.com>
>> wrote:
>>> Hi.. I needed a few tips on 2-D localisation of a sound source using 2
>>> microphones (COLLINEAR WITH THE SOURCE). The source is assumed to be a
>>> single frequency source and in-accessible with the only known
>>> characteristics being the ones measured from an oscilloscope.
>>> Oh, and I'm a Mechanical Engineer with ABSOLUTELY NO PRIOR EXPOSURE TO
>>> DSP
>>> so please be kind enough to elaborate those "few tips"...Thanks :-)
>>
>> Ford,
>>
>> Just to make sure we're working with the same impression, I'm
>> interpreting your phrase "COLLINEAR WITH THE SOURCE" this way:
>>
>> S: source
>> M1,M2: microphones
>>
>> A-----M1---------M2---------S-----B
>>
>> As Fred has pointed out, as stated this is a 1-D localization
>> problem, not a 2-D problem.
>>
>> And I'm assuming this is a "mathematical" problem (Oscilloscope has
>> infinite bandwidth and values can be read from it with infinite
>> precision, microphones are omnidirectional and infinitely small and
>> can be placed with infinite accuracy, instantaneous measurements,
>> etc.)
>>
>> S is a "single-frequency source" -- a simple sine wave with
>> frequency "F". You can measure F with the 'scope, which, with the
>> speed of sound in air will yield wavelength -- the length of one
>> full compression-rarefaction cycle from S.
>>
>> But... unless you have some way of causing a recognizable "hiccup"
>> from S -- starting and stopping it, for example -- I think I have to
>> go along with Fred: it's insoluble, at least as stated. You need
>> more information, such as "the position of S is known within a
>> one-wavelength distance", or "S starts and stops", or something
>> else.
>>
> Well, the intensity of a sound falls off as 1/(distance^2). Assuming that
> both microphones are on the same side of the sound source, let the amplitude
> of the sound as measured at the mics be A1 and A2 and the distance between
> the source and the mics be d1 and d2. Let the distance between the mics be
> d, and to simplify the math let A1 >A2 (and therefore d1 < d2). Call the
> amplitude of the sound at unit distance A.
> A1 = A/(d1^2)
> A2 = A/(d2^2) = (A/((d1+d)^2)
> so A1/A2 = (d1+d)^2/d1^2)
> (d1+d)/d1 = sqrt(A1/A2) = R
> d1+d = R* d1
> d = (R-1)* d1
> d1 = d/(R-1) = d(sqrt(A1/A2)-1)
Philip,
Well color me purple and call me an eggplant!
I was really enjoying these nice trees... where did this _forest_
suddenly appear from? <grin?>
There's still a bit of ambiguity in that, given S is a point source,
and it's also presumably invisible and in another room so you can't
"see" it or "listen" to it, you could be dealing with:
A----M2-------------M1-------S--------B
or
A----M2----------------------S--------M1-------B
but you do know that S is to the "right" of the microphone with the
weaker signal. Taking a third reading off to the "left" of _that_
microphone guarantees that you can combine its amplitude and the
amplitude measured at the microphone with the weaker signal, using
your forumlation, and trust the result.
This could explain why collinearity was introduced, although the
"amplitude" approach could equally handle a 2-D or 3-D location
problem. You'd just need to take more measurements.
I think I'll go fix another cup of tea (hopefully the results will
be slightly less embarassing <grin!>). Anyone see a way to solve
this with only two measurements?
Thanks, Philip.
Frank
--
"Science is not a linear march to truth but a tortuous road with
blind alleys and a rubbernecking delay every mile or two. Our
road map is not objective reality but the patterns of human
thoughts and theories."
-- Stephen Jay Gould, "Eight Little Piggies"
--
Frank McKenney, McKenney Associates
Richmond, Virginia / (804) 320-4887
Munged E-mail: frank uscore mckenney ayut mined spring dawt cahm (y'all)
Reply by Philip Martel●December 20, 20082008-12-20
"Frnak McKenney" <frnak@far.from.the.madding.crowd.com> wrote in message
news:856dnZH-b6KZjNDUnZ2dnUVZ_vSdnZ2d@earthlink.com...
> On Thu, 18 Dec 2008 17:02:32 -0600, FordPrefect <altermyego42@gmail.com>
> wrote:
>> Hi.. I needed a few tips on 2-D localisation of a sound source using 2
>> microphones (COLLINEAR WITH THE SOURCE). The source is assumed to be a
>> single frequency source and in-accessible with the only known
>> characteristics being the ones measured from an oscilloscope.
>> Oh, and I'm a Mechanical Engineer with ABSOLUTELY NO PRIOR EXPOSURE TO
>> DSP
>> so please be kind enough to elaborate those "few tips"...Thanks :-)
>
> Ford,
>
> Just to make sure we're working with the same impression, I'm
> interpreting your phrase "COLLINEAR WITH THE SOURCE" this way:
>
> S: source
> M1,M2: microphones
>
> A-----M1---------M2---------S-----B
>
> As Fred has pointed out, as stated this is a 1-D localization
> problem, not a 2-D problem.
>
> And I'm assuming this is a "mathematical" problem (Oscilloscope has
> infinite bandwidth and values can be read from it with infinite
> precision, microphones are omnidirectional and infinitely small and
> can be placed with infinite accuracy, instantaneous measurements,
> etc.)
>
> S is a "single-frequency source" -- a simple sine wave with
> frequency "F". You can measure F with the 'scope, which, with the
> speed of sound in air will yield wavelength -- the length of one
> full compression-rarefaction cycle from S.
>
> But... unless you have some way of causing a recognizable "hiccup"
> from S -- starting and stopping it, for example -- I think I have to
> go along with Fred: it's insoluble, at least as stated. You need
> more information, such as "the position of S is known within a
> one-wavelength distance", or "S starts and stops", or something
> else.
>
Well, the intensity of a sound falls off as 1/(distance^2). Assuming that
both microphones are on the same side of the sound source, let the amplitude
of the sound as measured at the mics be A1 and A2 and the distance between
the source and the mics be d1 and d2. Let the distance between the mics be
d, and to simplify the math let A1 >A2 (and therefore d1 < d2). Call the
amplitude of the sound at unit distance A.
A1 = A/(d1^2)
A2 = A/(d2^2) = (A/((d1+d)^2)
so A1/A2 = (d1+d)^2/d1^2)
(d1+d)/d1 = sqrt(A1/A2) = R
d1+d = R* d1
d = (R-1)* d1
d1 = d/(R-1) = d(sqrt(A1/A2)-1)
>problem is the periodicity of the (assumed) signal from S.
>
> Imagine that the location of S along AB is chosen as the origin, the
> 0 point for measuring displacements.
>
> Now imagine that M1 and M2 are placed anywhere along the line and
> you observe the signal from both (it's an imaginary 'scope, so I can
> imagine it's a two-channel 'scope <grin!>). Now imagine placing the
> mocrophones at any other locations and measuring again.
>
> Now imagine that I move S exactly one wavelength to the left, or to
> the right, and that you repeat the same set of measurements. Your
> 'scope traces will be identical... but your distances from S will
> be different. Oops!
>
> However, if you drop the collinearity assumption, you can get a
> _direction_ to S by putting M1 and M2 on a bracket and rotating them
> until the sine waves from 'scope channel 1 and 'scope channel 2 line
> up. Move perpendicular to this direction and repeat, then plot the
> bearings; and if you're working on a plane (flat surface) you have
> the location of S through "triangulation". (On a globe that will
> still leave you two possible locations for S, so you'll need at
> least one more measurement to pin it down; on other surfaces YMMV.
> <grin!>)
>
> (You'll see this approach used in all the "Find The Hidden Radio
> Transmitter" scenes of any spy movie. <grin!>)
>
> But, again, to do this violates the problem-as-originally-stated.
>
> So either your professor stated the problem badly, you copied it
> down incorrectly, or it really is impossible to solve. Or meybe
> there's a "gotcha" we've overlooked somewhere?
>
>
> Frank McKenney
> --
> I am Boris of Borg. Assimilate moose and squirrel.
> --
> Frank McKenney, McKenney Associates
> Richmond, Virginia / (804) 320-4887
> Munged E-mail: frank uscore mckenney ayut mined spring dawt cahm (y'all)
> So either your professor stated the problem badly, you copied it
> down incorrectly, or it really is impossible to solve. Or meybe
> there's a "gotcha" we've overlooked somewhere?
I think that the OP meant "coplanar" and is embarrassed to 'fess up.
Jerry
--
Engineering is the art of making what you want from things you can get.
�����������������������������������������������������������������������
Reply by Eric Jacobsen●December 20, 20082008-12-20
On Thu, 18 Dec 2008 17:02:32 -0600, "FordPrefect"
<altermyego42@gmail.com> wrote:
>Hi.. I needed a few tips on 2-D localisation of a sound source using 2
>microphones (COLLINEAR WITH THE SOURCE). The source is assumed to be a
>single frequency source and in-accessible with the only known
>characteristics being the ones measured from an oscilloscope.
>Oh, and I'm a Mechanical Engineer with ABSOLUTELY NO PRIOR EXPOSURE TO DSP
>so please be kind enough to elaborate those "few tips"...Thanks :-)
>
As others have mentioned, strictly getting position in general is
going to be difficult as you've described it. It gets easier if S
moves at a constant rate, since then you can use the Doppler to
estimate range (with some constraints). Since that's a pretty
limiting assumption, it's probably not very useful.
Eric Jacobsen
Minister of Algorithms
Abineau Communications
http://www.ericjacobsen.org
Blog: http://www.dsprelated.com/blogs-1/hf/Eric_Jacobsen.php
Reply by Eric Jacobsen●December 20, 20082008-12-20
On Sat, 20 Dec 2008 03:08:06 +0000 (UTC), glen herrmannsfeldt
<gah@ugcs.caltech.edu> wrote:
>Randy Yates <yates@ieee.org> wrote:
>> "Fred Marshall" <fmarshallx@remove_the_x.acm.org> writes:
>
>>> A mechanical engineer's trick for reducing machinery noise:
>>> Make the number of rotating elements a prime number (such as pistons in an
>>> engine). They will radiate in phase that is related by the prime number
>>> (we assume they are close together relative to a wavelength).
>>> The sum of the sinusoids will be a minimum compared to having more
>>> (nonprime) elements or fewer (nonprime) elements.
>
>> Why don't we see more 5- and 7- cylinder cars, then?
>
>The radial engines they used to use on airplanes were usually
>an odd number. For V engines, two pistons on each crank, it
>has to be even. It might be that you could do a V design with
>all but the last having two, and still arrange the phase.
>
>A V8 fires every 90 degrees of crankshaft rotation
>(on a four stroke/cycle engine), a V6 every 120 degrees.
>
>I believe there are three cylinder engines in some small cars.
>
>-- glen
Even in-line engines usually have even numbers of cylinders. It's
harder to manage vibration in a 3-, 5- or 7- cylinder engine than it
is with an even number of cylinders. Sometimes symmetry is a good
thing.
I can see how Fred's point makes sense, and pistons aren't always
easily treated as "rotating machinery". I don't think the same
principle applies with cylinders as it would with, say, keeping
vibration down in the shafts of a transmission.
Eric Jacobsen
Minister of Algorithms
Abineau Communications
http://www.ericjacobsen.org
Blog: http://www.dsprelated.com/blogs-1/hf/Eric_Jacobsen.php
Reply by Frnak McKenney●December 20, 20082008-12-20
On Thu, 18 Dec 2008 17:02:32 -0600, FordPrefect <altermyego42@gmail.com> wrote:
> Hi.. I needed a few tips on 2-D localisation of a sound source using 2
> microphones (COLLINEAR WITH THE SOURCE). The source is assumed to be a
> single frequency source and in-accessible with the only known
> characteristics being the ones measured from an oscilloscope.
> Oh, and I'm a Mechanical Engineer with ABSOLUTELY NO PRIOR EXPOSURE TO DSP
> so please be kind enough to elaborate those "few tips"...Thanks :-)
Ford,
Just to make sure we're working with the same impression, I'm
interpreting your phrase "COLLINEAR WITH THE SOURCE" this way:
S: source
M1,M2: microphones
A-----M1---------M2---------S-----B
As Fred has pointed out, as stated this is a 1-D localization
problem, not a 2-D problem.
And I'm assuming this is a "mathematical" problem (Oscilloscope has
infinite bandwidth and values can be read from it with infinite
precision, microphones are omnidirectional and infinitely small and
can be placed with infinite accuracy, instantaneous measurements,
etc.)
S is a "single-frequency source" -- a simple sine wave with
frequency "F". You can measure F with the 'scope, which, with the
speed of sound in air will yield wavelength -- the length of one
full compression-rarefaction cycle from S.
But... unless you have some way of causing a recognizable "hiccup"
from S -- starting and stopping it, for example -- I think I have to
go along with Fred: it's insoluble, at least as stated. You need
more information, such as "the position of S is known within a
one-wavelength distance", or "S starts and stops", or something
else.
The problem is the periodicity of the (assumed) signal from S.
Imagine that the location of S along AB is chosen as the origin, the
0 point for measuring displacements.
Now imagine that M1 and M2 are placed anywhere along the line and
you observe the signal from both (it's an imaginary 'scope, so I can
imagine it's a two-channel 'scope <grin!>). Now imagine placing the
mocrophones at any other locations and measuring again.
Now imagine that I move S exactly one wavelength to the left, or to
the right, and that you repeat the same set of measurements. Your
'scope traces will be identical... but your distances from S will
be different. Oops!
However, if you drop the collinearity assumption, you can get a
_direction_ to S by putting M1 and M2 on a bracket and rotating them
until the sine waves from 'scope channel 1 and 'scope channel 2 line
up. Move perpendicular to this direction and repeat, then plot the
bearings; and if you're working on a plane (flat surface) you have
the location of S through "triangulation". (On a globe that will
still leave you two possible locations for S, so you'll need at
least one more measurement to pin it down; on other surfaces YMMV.
<grin!>)
(You'll see this approach used in all the "Find The Hidden Radio
Transmitter" scenes of any spy movie. <grin!>)
But, again, to do this violates the problem-as-originally-stated.
So either your professor stated the problem badly, you copied it
down incorrectly, or it really is impossible to solve. Or meybe
there's a "gotcha" we've overlooked somewhere?
Frank McKenney
--
I am Boris of Borg. Assimilate moose and squirrel.
--
Frank McKenney, McKenney Associates
Richmond, Virginia / (804) 320-4887
Munged E-mail: frank uscore mckenney ayut mined spring dawt cahm (y'all)
Reply by glen herrmannsfeldt●December 19, 20082008-12-19
>> A mechanical engineer's trick for reducing machinery noise:
>> Make the number of rotating elements a prime number (such as pistons in an
>> engine). They will radiate in phase that is related by the prime number
>> (we assume they are close together relative to a wavelength).
>> The sum of the sinusoids will be a minimum compared to having more
>> (nonprime) elements or fewer (nonprime) elements.
> Why don't we see more 5- and 7- cylinder cars, then?
The radial engines they used to use on airplanes were usually
an odd number. For V engines, two pistons on each crank, it
has to be even. It might be that you could do a V design with
all but the last having two, and still arrange the phase.
A V8 fires every 90 degrees of crankshaft rotation
(on a four stroke/cycle engine), a V6 every 120 degrees.
I believe there are three cylinder engines in some small cars.
-- glen
Reply by dbd●December 19, 20082008-12-19
On Dec 19, 10:33 am, "Fred Marshall" <fmarshallx@remove_the_x.acm.org>
wrote:
.> ...
.> A mechanical engineer's trick for reducing machinery noise:
.> Make the number of rotating elements a prime number (such as
pistons in an
.> engine). They will radiate in phase that is related by the prime
number (we
.> assume they are close together relative to a wavelength). The sum
of the
.> sinusoids will be a minimum compared to having more (nonprime)
elements or
.> fewer (nonprime) elements.
.>
.> Fred
Aside from certain types of engines sometimes found in aircraft:
http://en.wikipedia.org/wiki/Rotary_engine
I was not aware that pistons were rotating elements.
Dale B. Dalrymple