Harry Olson's Throat Impedance Equations and PWK's

[WMcD]

In the archive of PWK's papers (if there is one) is there any correspondence between  PWK and Harry Olson Ph.D which corrected an equation used by Olson for throat impedance?  Long story.  I'll set out what I've determined at the risk of being boring. OTOH, I've done a lot of homework before posing the question.

 

I've been analyzing PWK's 1945 paper which is aimed at the non-zero throat impedance of a finite horn below cut-off.  The goal must have been to address how the K-Horn will produce bass below fc. 

 

PWK also presents Olson's equation as a starting point and then his variations on Olson's equation (this uses tangents).  PWK says this is arrived at "after a few mathematical steps" which PWK does not describe but I've recreated, or at least found steps reaching PWK's results. This requires a lot of trig identities and information supplied by a book by Irving Crandell, Ph.D. from Bell Labs.

 

( I also find what could be errors in the article but maybe non-critical.)  Was there an errata sheet?

 

A closely  related matter is that Olson used two different equations over the years.  One appears in his earlier works including "Elements of Acoustical Engineering" (let me say, from the 1930's) which PWK starts with in 1945. I'll call that Olson I. The other equation, which I'll call Olson II appears in the larger later work by Olson of Acoustical Engineering (let me say, from the 1950's).  The change is actually just a matter of a plus, versus minus in two factors.  You see Olson II (or a normalized version) in at least one paper by Don Keele and widely elsewhere. This "sign" may seem minor but it is a real headache in making actual calculations.

 

Returning to PWK's equation above cut-off, he says that (a/b) which appears in two terms must be taken as minus above cut-off.  Following in PWK's footsteps in reaching the tangent - based equation, this should not be required.  But graphing the results is erroneous without this.  Further, back tracking the effect of this (a/b) taken as minus leads to the second form, that being  Olson II.

 

Going back to the very first pilgrimage (February 16, 2001 for the unveiling of the Jubilee) Jim Hunter showed us a small book (brown cover?) owned by PWK (still with us, then of course), which might have been "Elements."  It had PWK's pencil corrections to some printed equation in the book and it might have been Olson I.  Jim mentioned that this showed how PWK corrected something Olson had written.  All this is IIRC, of course.

 

Just maybe, PWK wrote to Olson saying his equation was wrong, and Olson corrected it.  I also wonder how Olson would up with the erroneous "Olson I" though this might involve solving a couple of complicate differential equations.  I also see that Bell Labs calculated the throat impedance of the big bass box as shown in the Symposium paper of the Klipsch papers collection.  I've recreated the results pretty closely  They must have used the correct equation. though it is not set out.

 

I'd love to write a technical article which includes an analysis of correspondence between these two masters of the horn.  Because it is tribute to PWK and adds human interest.

 

Any information is welcome.

 

WMcD

 

 

[Travis In Austin]

Gil, that  is quite a question, one that may put Mr. Hunter to task.  I have forwarded that question to him for a response. 

 

A question as specific as yours, and as technical, may evoke one of 3 responses from Mr. Hunter:

 

1.  He has digitized this information, he knows the answer, and has other information from other sources that expound on your question.

 

2.  He will need time to get you a full and complete response.  One thing I know from observing The Historian is that he epitomizes the word historian.  He will not guess, he doesn't add spin, and he won't try and guild the Lily.  If he partially knows the answer he tends to wants to get the full answer before giving a response. 

 

3. He doesn't  know, and he doesn't have another source to try to find the answer.  If he doesn't know, and if there is no real way of knowing, he will say that unfortunately the records (so far) are not available to answer the question.  He has scanned literally thousands upon thousands of paper documents and indexed them.  At the last Pilgrimage he gave a 2 hours slide show "sneak preview" of documents he had discovered in his excavations such as a letter from PWK to the President of the United States (don't quote me, I believe it was LBJ) complaining about Daylight Savings Time.  

 

As you have mentioned, The Historian is the one person I know that could even approach giving that question an answer it deserves.

 

Travis

 

[WMcD]

Thanks Travis.  I understand completely.

 

BTW, I prefer WMcD here or "Gil".  Family nickname.  Never "Bill."

 

I was not aware of the extensive work by Mr. Hunter which you describe.  Is there an Accutron watch story and some temperature sensitive calculator story in there someplace?  Smile.  Just a quip.  Not a request for info on these.

 

It seems to me that PWK must have gotten requests from armchair nincompoops with theories that would require a hundred hours of work by PWK to debunk.  And therefore PWK might have just ignored them.  Jim Hunter might be in a similar situation.

 

I don't expect Hunter to do calculations or anything of course.  There could be sort of a human interest, or engineering interest, story, though.  Again, one which will reveal a little known contribution by PWK to audio. 

 

WMcD

 

 

 

 

[Travis In Austin]

7 minutes ago, WMcD said:

Thanks Travis.  I understand completely.

 

BTW, I prefer WMcD here or "Gil".  Family nickname.  Never "Bill."

 

I was not aware of the extensive work by Mr. Hunter which you describe.  Is there an Accutron watch story and some temperature sensitive calculator story in there someplace?  Smile.  Just a quip.  Not a request for info on these.

 

It seems to me that PWK must have gotten requests from armchair nincompoops with theories that would require a hundred hours of work by PWK to debunk.  And therefore PWK might have just ignored them.  Jim Hunter might be in a similar situation.

 

I don't expect Hunter to do calculations or anything of course.  There could be sort of a human interest, or engineering interest, story, though.  Again, one which will reveal a little known contribution by PWK to audio. 

 

WMcD

 

 

 

 

I dictated it Gil and it came out, well I have changed it just the same.

 

I am very interested in The Historian's response.  I am betting he pulls a rabbit out of his hat and has a mind blowing answer.

 

Travis

[dtel's wife]

From Jim Hunter:

 

I will not address the mathematics (way too rusty), but I will give just a little peek at our correspondence files.  Olson was an NIH kind of guy (not invented here).  It shows up as early as 1945 in an exchange regarding incorrect references in the first edition of Elements of Acoustical Engineering.  Later in 1947, PWK wrote to Olson encouraging him to publish an updated book.  The tone was very respectful.  The 2^nd edition eventually came out, but it did not credit Paul with the “new equation”.  There are several letters to other audio engineers lamenting this apparent snub by Olson.  In 1961 he wrote to William Snow (Symposium on Auditory Perspective guy) that included a comment regarding his 1945 paper’s correction of Olson’s horn theory.  Olson’s snubbing may have been the impetus for “How Not to Have Stereo”.

 

The most recent correspondence demonstrating this NIH factor was a three-way dialog in 1973 between PWK, Olson, and Richard Small (Thiele/Small parameters guy).  It was a circular critique of the drafts of Small’s first major paper.

 

I have not found “errata” on the 1945 paper, but I have a long way to go in fully exploring PWK’s archives!

 

 

610424 How Not to Have Stereo.pdf

Olson.pdf

[JRH]

11 hours ago, WMcD said:

Thanks Travis.  I understand completely.

 

BTW, I prefer WMcD here or "Gil".  Family nickname.  Never "Bill."

 

I was not aware of the extensive work by Mr. Hunter which you describe.  Is there an Accutron watch story and some temperature sensitive calculator story in there someplace?  Smile.  Just a quip.  Not a request for info on these.

 

It seems to me that PWK must have gotten requests from armchair nincompoops with theories that would require a hundred hours of work by PWK to debunk.  And therefore PWK might have just ignored them.  Jim Hunter might be in a similar situation.

 

I don't expect Hunter to do calculations or anything of course.  There could be sort of a human interest, or engineering interest, story, though.  Again, one which will reveal a little known contribution by PWK to audio. 

 

WMcD

 

 

 

 

 

See the following for the Accutron story.

http://www.klipsch.com/accutron

[JohnA]

Love the "How Not To Have Stereo" paper!  Mr. Paul is correct, of course, and I now have my Big, Old Klipsch.  But if it had not been for my parents' turntable in a cabinet and the 2 cu ft box, that I could afford in college, I would not have had the music obsession I have that lead me to Klipsch. 

 

[JohnA]

5 hours ago, JRH said:

 

See the following for the Accutron story.

http://www.klipsch.com/accutron

 

Wave a red cape in front of a bull and whaddaya get? 

 

I have a similar encounter with a very cool mechanical watch displaying the internal mechanism.  However, I just took it back to the store.  LOL!  I just don't have the patience to futz with the manufacturer like that. 

[dtel's wife]

What a man!!  

[avguytx]

That was a great read. 

[WMcD]

Thank you very much Jim, and Dtel's Wife for passing it along.  It confirms my suspicions.

 

Jim did pull a rabbit out of his hat.  From the speed of response, the cute rodent must have been near the top.  Though I'm sure he did a lot of work in any case.

 

I was not aware of the second edition of "Elements."  After some research I located it at a library within walking distance of my home. Head slap by me.

 

The change by Olson might have otherwise been sort of (as often cited by the Car Talk brothers) a post hoc ergo propter hoc matter.  See https://en.wikipedia.org/wiki/Post_hoc_ergo_propter_hoc  OTOH, Jim's report makes it cause and effect.

 

"How Not To . . . " is wonderful.  It just shows that PWK with a slide rule is force to be contended with.  Add a typewriter and watch out! 

 

Best,

 

WMcD