If the speed of sound is constant, how can any wavefront _not_ be spherical at a distance sufficiently large compared to the radiating surface's diameter?
The flat wavefront assumptions from the early days were glaringly wrong in hindsight. In the early 1980's my father developed a method of successive iteration to design an exponential area horn wall with spherical wavefront. It was before serious personal computers, so he divided the length down the wall into 500 segments and made 500 HP calculations. (He had retired after doing turbine blade design and was enamoured of the prospect of personal computing. Didn't live quite long enough to see the Internet explosion.)
Thanks,
Chris
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Shockley was a clever and complex character, quite a promoter. Anyone in here old enough to remember his four-layer diodes? I mean, besides meAnd then he associated himself with the genius sperm bank stuff, hilariously parodied on Saturday Night Live when Rodney Dangerfield hosted.
Bardeen was amazingly bright and insightful, apparently rather self-effacing, and is the B of the BCS theory of superconductivity. To date he remains the only double-Nobelist in the field of physics.
Shockley - Too many blows to the head. I had a prof that worked directly with Shockley in the 60's, he had a serious car accident and was never the same. Only after this did he dwell on his racist theories.
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I was reading about this. According to wikipedia, Bardeen and Brattain have created the point-contact transistor, while Shockley invented and patented the junction transistor.
William Shockley - Wikipedia, the free encyclopedia
thx
alex
Thank you DF96
I was reading something very interesting on Heaviside.
http://archive.org/download/electromagnetict03heavuoft/electromagnetict03heavuoft.pdf
Vol. III, pages 149-152 (p. 152-154 explanation and p.154-158 derivation)
George
Chris
Speed of sound in air is not fixed (constant). Even if we consider air as an ideal gas and as a non-dispersive medium and assume adiabatic conditions, still local temperature variations will vary sound speed.
Speed of sound - Wikipedia, the free encyclopedia
George
Very interesting.
Vladimir Arnold, the late great dynamical-systems theorist, late in life had a serious car accident as well and was never quite the same, according to my friend John Norris who had worked with him. Fortunately he retained his aplomb and great sense of humor, and his contributions were prodigious before his output slowed.
Head injuries often bring about funny changes. My mother, a widow, suddenly got extremely (for her children, scandalously) affable and interested in men again in her mid-eighties, after a fall and subsequent life-threatening cranial hematoma was caught barely in the nick of time. In earlier life after such traumas, many switch interests abruptly from hard science, law, etc. to gastronomics, art, music.
Heaviside had a reputation for annoying people, especially mathematicians and electrical engineers who for opposite reasons thought his work was wrong. Mathematicians said his work lacked rigour (true) and therefore must be wrong (not true). Engineers said his results were counter-intuitive (true) and therefore must be wrong (not true). Eventually the mathematicians found a way of accommodating his ideas into proper mathematics, and the engineers found that his results actually worked in real life (later on, they learned enough maths to understand his calculations too).
However, that fact that his results were correct does not necessarily mean that the semi-mechanical reasoning he used to guide his maths is also correct. He could not conceive of a wave without a medium. We can.
However, that fact that his results were correct does not necessarily mean that the semi-mechanical reasoning he used to guide his maths is also correct. He could not conceive of a wave without a medium. We can.
I love the beginning of that third volume and the story of the boy. For some reason I couldn't scan it adequately and deleted the post after noticing lines of type were cut off. I have the three volumes in storage so maybe I'll dredge them up and scan directly.
Other visionaries of the pre-relativity and quantum theory era, William Thomson (Lord Kelvin) and Peter Guthrie Tait, had some theories about "vortex atoms" that they advanced to explain many things. There is an eerie similarity between some of their topological notions and recent physical theory.
EDIT: here's a reference link to an nice paper about this: http://www.csee.umbc.edu/~lomonaco/kelvin/kelvin23.pdf
Other visionaries of the pre-relativity and quantum theory era, William Thomson (Lord Kelvin) and Peter Guthrie Tait, had some theories about "vortex atoms" that they advanced to explain many things. There is an eerie similarity between some of their topological notions and recent physical theory.
EDIT: here's a reference link to an nice paper about this: http://www.csee.umbc.edu/~lomonaco/kelvin/kelvin23.pdf
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Well, sure, but it's constant enough for designing horn wall contours, in any place where people would be comfortable. Incidentally, for an exponential (on center line distance from small end) area expansion wave front contour is the involute of the horn wall with a flat central disc the size of the small end and the wave front is normal to the horn wall, for true (spherical) wavefronts.
Thanks,
Chris
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New IMD article
Since IMD and similar topics recur frequently in this thread, here is an interesting article on IMD:
IMD - Something New
Since IMD and similar topics recur frequently in this thread, here is an interesting article on IMD:
IMD - Something New
Nonlinearities that produce the third harmonic of a single sinusoid will produce IM products from f1 and f2 at 2f1- f2 and 2f2 - f1. You need a nonlinearity that will generate some second harmonic distortion from a fundamental, to generate |f1 - f2| and f1 + f2.
I'm surprised he couldn't find ample discussions of this.
BTW, this is a reason why second harmonic distortion is not so benign, unless you are listening to very sparse textures, like solo voice or other solo instruments. High frequency IM will generate difference-frequency energy often in regions of high aural acuity. Not good.
Here it is:
Volume III starts sarcastically and ends wisely ("Limitations on Scientific Prediction." p. 518-519)
George
Thanks for this fireworks. I wish I still had my copy of the B&K 1902 manual where I had scribbled the equivalences of Harm. Dist. to each type of IMD test. I've insufficient brain cells left to redo the maths.
When I did this in the early 80's, I couldn't find any sources for the maths either.
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I agree Rod is a fun guy but this stuff has been hashed over from just about any angle somewhere. I assume his use of the term non-harmonic does not mean he believes in the creation of frequencies that are not n*f1 +- m*f2.
I'll have to read the whole thing.
EDIT - I read the whole thing. I like Rod but here he is speaking from a fairly hermetic naivete. You can derive all these results from a simple mathematical exercise, his comment about not being able to offer any references because there are none is baffling.
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