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Infinite Line Source: analysis
Infinite Line Source: analysis
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Old Today, 03:29 AM   #241
Dave Zan is offline Dave Zan  Australia
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Join Date: Nov 2010
Quote:
Originally Posted by werewolf View Post
As i see it ... we can analyze any source with constant volume velocity OR constant volume acceleration. I chose constant volume acceleration...
Yes, your analysis in terms of volume acceleration seems totally reasonable to me, for the reasons you stated.
But in those terms the plane source has a hell of a tail, it's infinite!
So to say the point source has no tail with (constant) volume acceleration, the line source has a tail in volume acceleration and the plane source has no tail in terms of volume velocity seems inconsistent.

Best wishes
David

Last edited by Dave Zan; Today at 03:33 AM.
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Old Today, 03:38 AM   #242
werewolf is offline werewolf  United States
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Location: Austin, TX
Quote:
Originally Posted by Dave Zan View Post
Yes, your analysis in terms of volume acceleration seems totally reasonable to me, for the reasons you stated.
But in those terms the plane source has a hell of a tail, it's infinite!
So to say the point source has no tail with (constant) volume acceleration, the line source has a tail in volume acceleration and the plane source has no tail in terms of volume velocity seems inconsistent.

Best wishes
David
Only when we consider the sources to be constant volume velocity, do the even-numbered dimensions (for sources) create tail-less impulse responses ... that's my story and i'm sticking to it

Happy to be proven wrong, of course !!
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Old Today, 03:54 AM   #243
Dave Zan is offline Dave Zan  Australia
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Quote:
Originally Posted by werewolf View Post
Only when we consider the sources to be constant volume velocity...
Doesn't this contradict your own excellent reasons to chose constant volume acceleration?

Quote:
I chose constant volume acceleration for the Point Source to begin with, because : first, it represents the behavior of most transducers (speakers) with which we're familiar (above resonance)... and second, it achieves the "flat" frequency response...
Like you, I am interested in Earl's take on this.

Best wishes
David
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Old Today, 04:25 AM   #244
werewolf is offline werewolf  United States
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Join Date: Feb 2004
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Quote:
Originally Posted by Dave Zan View Post
Doesn't this contradict your own excellent reasons to chose constant volume acceleration?
No contradiction at all!

One can choose to analyze sources with constant acceleration, velocity or displacement. No selection among these is "wrong" ... i just think that one choice is more directly connected to the way we typically operate transducers. Doesn't make the other ways "wrong".

All i've done, is develop some math to prove, or disprove, Earl's contention that sources in even dimensions have no impulse response tail. And i've found that this IS true, if sources are analyzed with constant volume velocity ... which is, i think, the preferred choice for physicists

That's all

Last edited by werewolf; Today at 04:29 AM.
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Old Today, 07:06 AM   #245
Dave Zan is offline Dave Zan  Australia
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Join Date: Nov 2010
Quote:
Originally Posted by werewolf View Post
All i've done, is develop some math to prove, or disprove, Earl's contention that sources in even dimensions have no impulse response tail. And i've found that this IS true, if sources are analyzed with constant volume velocity...
But if we do this for the point source then isn't the response the "derivative" of an impulse rather than an impulse?
(I realize that to "differentiate" a Dirac Delta strictly we need hyperfunction theory, or maybe distributions will do, so I won't even try to be formally correct.)
So it would not preserve waveshape in that domain?

And it looks that as you add dimensions you would next have to use constant volume displacement, and so on, it's not an odd/even alternation.

My concern is not whether a constant volume velocity or constant volume acceleration is the "correct" analysis, as you say, we can chose to suit our purpose.
My concern is consistency.
No fair to compare a CVA analysis of a point source with a CVV of a plane
Have you done an analysis of a point source with CVV?
That would be better than my shonky differentiation of an impulse

Best wishes
David

American spellcheck doesn't know "shonky" : untrustworthy, maybe crooked, underhand, devious.

Last edited by Dave Zan; Today at 07:07 AM. Reason: Syntax
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Old Today, 08:13 AM   #246
werewolf is offline werewolf  United States
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Join Date: Feb 2004
Location: Austin, TX
Quote:
Originally Posted by Dave Zan View Post
But if we do this for the point source then isn't the response the "derivative" of an impulse rather than an impulse?
(I realize that to "differentiate" a Dirac Delta strictly we need hyperfunction theory, or maybe distributions will do, so I won't even try to be formally correct.)
So it would not preserve waveshape in that domain?
In electrical engineering, we differentiate Dirac impulses all the time ... the result is an impulsive "doublet" A positive-going impulse, immediately followed a negative-going impulse, all at t=0 (most easily seen by constructing a single impulse, in the limit, as a finite pulse getting "narrower" and "taller" ... and watch the derivative as you go). Still ... no tail!
Quote:

And it looks that as you add dimensions you would next have to use constant volume displacement, and so on, it's not an odd/even alternation.
yeah i got nuthn ...
Quote:

My concern is not whether a constant volume velocity or constant volume acceleration is the "correct" analysis, as you say, we can chose to suit our purpose.
My concern is consistency.
No fair to compare a CVA analysis of a point source with a CVV of a plane
Have you done an analysis of a point source with CVV?
That would be better than my shonky differentiation of an impulse

Best wishes
David

American spellcheck doesn't know "shonky" : untrustworthy, maybe crooked, underhand, devious.
Exercises left to the reader ... please feel free to pursue, even in this thread but fair warning ... typing all those equations (with selective bolding) is no small task
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