Need an algebra guru's help, do we have any?

[Way2slow]

I have some algebra that's not making a lot of since to me and it has been over 45 years since I've had to do much algebra.  That was when I got my EE degree.

I'm learning how to make Native American Style Flutes and there is a section in one of the books I'm studying on how to figure playing hole size and placement that's kinda kicking my butt.

I will probably have to make a copy of the pages and email them because I don't know how in the heck I could explain it on here.

[islandbass]

Send it my way. I haven’t done math in any capacity for decades now but I have been helping my daughter with college level “algebra”. I am amazed that I still remembered a lot of it and if I didn’t, a quick read of her book and I was like, “oh right. I remember, lol.”

 

I am am hoping to make what is called a hegalong and I know nothing about how to make it. Interestingly enough, whatever mathematics is involved for making this flute might come in handy and at least be some good mental exercise. Send it to me. 

 

I did study some EE back in the day but don’t ask me about making a thevenin equivalent circuit, alright, lol? 

 

valemax154avvm@rocketmail.com

[tbone1993]

wolfram alpha

 

[islandbass]

23 minutes ago, tbone1993 said:

 

wolfram alpha

 

That is a very interesting app and I hadn’t heard of it. I was nearly tempted to get it but I feared I might use it too much as a crutch if it is that good of an app. So until my mental and physical faculties fail, I will continue to use my brain and two hands to do most everything. Maybe I’ll buy that app when I turn 75, lol.

 

If if my son decides to pursue something in the stem field, I’d get it for him. Thanks for sharing. 

[Way2slow]

OK, I'm going to try posting the pages here.  There are three more pages need to make this one make since but this is a sample of where I'm at.  At the bottom of page 58 you will see the line: Solving for S2 and S5 and the figures S2= 1.171 and S5=1.097.  (That's not really S but the S is the closet thing on the keyboard to match the symbol he uses).  I can't for the life of me figure out where he came up with those figures. 

The site limits the size of inserts so I will have to make each page a separate reply, I can't get two pages in the same reply.  This is also not a real clear book so this is the best I can do for a copy. 

I will post one more page with a little background on the equation.  

 

[Way2slow]

This is the initial equation but there are two more pages with the supporting info.  If you think you can help, I will post the other two pages or email all four.  I suspect and email copy would be larger and more readable, but I figured I would let you see what's involved first.  You might want to recant your offer after seeing what's involved.

 

What this is, is called the bore extension and is needed for placement of the playing holes.  This is an unknown until you solve for it.  The playing hole sizes are also unknowns but hole two and hole five need to be at least 50% of the bore diameter of 3/4" or .75".  So that gives the size of hole 2 and hole 5 of 3/8" or .375".  Using those a knowns, you are supposed to be able to figure out S2 and S5 from that. 

You have to be able to come up with one of the S sizes to make the calculations for the other holes.  Once you have one, then you can solve for the others but I can't figure out how he solved for those first ones in 2 and 5.

[.ghoti.]

Thevenin? Yikes!

[EGbassing]

I'll try, but I just finished my first algebra course (still fairly basic) so I can't promise that I'll be able to solve it if it's complicated (I'll do my best though) I can also try to ask my brother if I can't figure it out because he's doing precalculus right now and has a vast wealth of algebraic knowledge indeed. ?

[Boomstick]

I can hardly see it past the smudging but is that symbol the derivative aka a calculus symbol?

 

I was a math minor in college (and short of what I could transfer, I was probably a course or two from being a math/dual major), but it's been years since I've used this in a daily basis.

[islandbass]

It is a bit hard to read but if the algebra involves only solving for one variable or simply plugging in values, it should be straight forward. 

 

I wonder if taking photos of the work he work and sending to us via email might be easier. I’ll look into this after I wash the dishes (really), lol. 

[islandbass]

@Way2slow: I reviewed the information on page 35 and what is written is straight forward geometry. However, I cannot find anything on that page clarifying what the following variables mean:

1) "R" (capital R)

2) that funny "l" or is that a one? I'm hoping it's the number "1" 

 

Please send me via email the 4 pages.

 

 

 

[Way2slow]

OK. that symbol you say looks like and l, is actually his own symbol to represent the distance from the antinode to the center of the playing hole.  For a while that I thought it was the "!" for a factorial and that was really confusing me.  I finally came to the conclusion it's just the sorry printing and it's that very elongated Z (kinda like a lazy Z) with curved ends looking symbol he uses for part of the hole placement measurement.   At least that's what I'm hoping it is because if it's a factorial symbol, I'm totally screwed.  I first said I would use the capitol S but the Z is more along the lines of how it's shaped.

For the R, No where in the book does he give a meaning for capital R other than above that equation where he is talking about the radius "r" for the volume of air moving tangentially. 

I think the guy was some sort of aeronautical engineer or something and he goes through pages of formulas where he keeps breaking them down into "simpler" versions and explaining each along the way.  You spend 20 minutes working a formula, just to learn that's not the one you will use because he breaks it down even more in another section.  I think he's just showing how he came up with the formula at the bottom of page 35 for (1+D/4)  in the formula (D/2) squared times Pi, divided by (Z+d) (1+D/4).  Note: I will us the capital "Z" to represent that funny shaped symbol of his own you will see a lot of, that is not a 1 or l in the equations.  That one measurement is the one creating all my heartburn.

The "Z" is the distance from center of playing hole to antinode.

the "d" is the difference in frequency wavelength between the sound hole (finger hole) being open vs closed.  The sound wave produces what's called a node and an antinode. The node is at the center of the wave and the antinode is at the end of the wave.  If a finger hole is in either of these two locations, bad things happen to the sound.

Everything is adjustable and you can play with the numbers, hole size and spacing between holes, etc. but you have to be able to calculate the antinode "Z" . 

At the bottom of page 58 he shows he solved for Z2=1.171" and Z5=1.097".  Those two holes he say need to be 1/2 the bore diameter so he used the known 3/8" (.375).  Once you get one, you can solve for the rest but I can't figure out how he got those.

I made a photo scan of this page and used my photo editor to see if it show up better so you can see better what things are.

One note: the top of the page says 2 & 4 should be the size of E, but then it shows 2 & 5 else where.  Anyway, "E" is the width of the true sound hole "TSH" which should be 1/2 the bore diameter. 

Keep on, I'm gonna have you making a flute. 

Also, the K1 at the end of the flute. That is a false length that's figure for the sound wave as it exits the end of the flute, which in this case is .25".

 

Now, if you are still game, I can try to scan the other pages as a photo's and see if they are more readable.

 

 

[islandbass]

Thanks. I think that this extra information from the image and what you provided will help. To be honest, I don't think your math skills are gone or lacking. The author seemed to love rehashing and simplifying things to the point he never needed to "go the long route" so to speak. It reminded me somewhat of finding the derivative the "long way" when you should have told me the derivative of  5x^3 is 15x^2, lol. Remember that? Honestly, I don't know why I do. 

 

I noticed the same thing reading the author's words.  Engineers don't mind the extra mathematical details, but I think this guy must be a mathematician at heart because only a mathematician would enjoy or fully appreciate the elegance and beauty of such simplification AND be so ready to share it with others, lol. I had one college prof who was like that.

 

He said, how many of you are EE majors? I raised my hand as did many others.  The answer to a problem was the square root of 2 (yeah, with the radical symbol, that looks like an adopted step brother of the division sign).  Do you know why we write this as the square root of 2? Why don't we write this a 1.414...? It went from that to imaginary numbers and that EE "love" to deal (his words) with them, and back to something about trigonometry. I honestly don't know how he fit all that math onto the chalkboard and still be so neat. It was a great ride, but he did forget to teach the day's lesson, lol.

[Way2slow]

Well if you are game here's the rest of the story. I reduced them down more and made better images so hopefully they work.  Where he solved for Z2 and Z5 at the bottom of page 58 is where I'm lost and can't find how it came up with those figures, and those are the starting blocks for the whole configuration.

[jbsoonerfan]

Just imagine if the original math was wrong.

[islandbass]

1 hour ago, jbsoonerfan said:

Just imagine if the original math was wrong.

Holy smokes. If I were drinking something, I would have spit some of it out and some if it might come out of my nostrils, laughing so hard. 

 

Thanks for the info, way2. I’m tied up over the weekend but looking forward to digging in.  If jbsoonerfan turns out to be right, you’ll be hearing me laughing and crying all the way from Seattle. 

[BASS302]

2 hours ago, jbsoonerfan said:

Just imagine if the original math was wrong.

I think you are right.  Hopefully you can read my math (I typed it in word, then did a snip, and attached as a jpg.  I assumed the "funny" symbols were actually lower case letter "L" representing length.

 

 

Using the quadratic formula to solve for L is an exercise left for the reader.  (I seem to remember that type of statement in my math books).

[Kev-mo]

Am I the only one thinking about how the Native Americans made them w/out algebra and you need to find a Native American?

[Way2slow]

Bass302, thanks, to was a lot of work.  It's taking me a little time to decipher all that and a little hard to understand being in the format you had to use to get it posted, but don't worry, I will get through it. 

I've tried several ways to get into my TI-84 Plus to see if that helps but I'm kinda rusty on programming that thing also.   I do greatly appreciate the work you put into it though.

 

Kev-Mo, the native Americans had elders with generations of knowledge that was passed down to them.  Us dump*** white folks were too busy trying to kill them all to pick up on that, and to busy figuring out ways on how to rip off everyone else to take time to teach something if there wasn't money involved.

[BASS302]

@Way2slow

I solved for L2 and L5 three times, and kept getting L2=1.1758 and L5=1.1024 and was puzzled about what I was doing wrong.  I took a shower, then solved twice more with the same L2=1.1758 and L5=1.1024.  I couldn’t figure out why I didn’t get the same answers as you showed were listed in the book.  I logged back on to BR to find out if anyone had answered, and saw the reply from @jbsoonerfan

The light bulb went off in my head that the author's answers might be incorrect, so I plugged the author’s answers into his own problem and found out that the authors answers are wrong for his own equations (if you plug his answers into his equations, you get a value of .613, not the .610 listed in his equation).  I guess you can’t believe everything you read!

What I did was to get the author’s equation into the form 0 = ax^2 + bx + c.  Then you can use the quadratic formula we all were taught in school, to solve for x (in this case x would be the “L” values).

So a = iK

     b = (idK-i +1)

     c = -id

(use the values for i, K, and d that I listed in my previous reply to calculate a, b, and c)

Out of curiousity, what happens if the holes are not in exactly the right place?  Does it make the flute out of tune?

Let us know how your flute turns out.  Good luck.

 

[Way2slow]

I have found a number of his answers that are off by several thousandths every time and way I can run them.  I assume that has to do with how he rounded and I rounded.  That however is not a problem.  It's almost impossible to measure and drill a hole that exact anyway.  To compensate for that, you drill about a 3/16" pilot hole and then just start going larger little by little, checking the frequency each time, until you get the hole in tune.

 

Bass302, I really appreciate all the effort you have put into my puzzle.  What I'm doing for a work-around is I programmed all the formulas into my TI-84+ and just plug in numbers until I get something that works and I like for a finger hole size and space.  A bit of a pain, but it gets me to the outcome I need

 

The distance between the finger hole and the antinode or node determines the size finger hole.  If the hole is too small it won't have much volume, if too large, you have trouble covering it with your finger.

Also, if you are too close to the node or antinode, if it makes a note, it will sound terrible. 

 

Off by a 10th of and inch and you just ruined a flute you spent a lot of time and effort into making.   Off by several thousandths and the whole size or spacing may no be usable, fingers can only stretch so far.