Issue Versions of Augspurger Tables

[villastrangiato]

Mr. Augspurger is quoted at the top left hand portion of page 429 in his paper "Loudspeakers on Damped Pipes"


"This is clearly shown in Fig. 6, which is the analog response of a small automotive loudspeaker on a .78 meter pipe. This is nominally a 109 hz pipe, but it actually resonates at 100 hz, which is also the loudspeaker's cone resonance. The light solid line represents cone output, the dashed line is pipe output, and the heavy solid line is the combined system response. Note that the upper resonances and antiresonances fall at exact 100 hz intervals."

Mr. Augspurger's analysis is clearly somewhat limited in this respect - he doesn't seek to explain why he's observing this phenomenon - he's just announcing it's presence.

Mr. Natkaniec's paper, which Mr. King suggested we all delete from our hard drives, does seek to answer this very question. And in my opinion, he does so accurately and eloquently.

[MJKing]

"This is clearly shown in Fig. 6, which is the analog response of a small automotive loudspeaker on a .78 meter pipe. This is nominally a 109 hz pipe, but it actually resonates at 100 hz, which is also the loudspeaker's cone resonance.

The pipe resonating at 100 Hz and not the calculated 109 Hz is most likely due to not including an end correction, resulting from the acousitc impedance boundary condition at the open end, when the quarter wavelength resonant frequency was estimated using the pipe's geometric length. So the pipe resonates at 100 Hz and has harmoncs at odd multiples of this frequency. Calculations and test results will never match exactly but they typically are close. These results are consistent with his paragraph which I included in the previous post.

[villastrangiato]

Yeah, Martin what's 3 or 4 inches of length on a 30 inch pipe anyway? We'll just put that one in the equation fudge factor and mark it as the "K" constant....
:rofl:

[Dennis H]

I think most trombone players would be surprised to learn that moving the slide doesn't do anything.

One of Martin's papers addresses all the issues raised so far in this thread. His other papers look good too but I haven't read all of them.

http://www.quarter-wave.com/TLs/TL_Anatomy.pdf

My simplistic way of looking at the quarter wave thing is there's a pressure decrease when the pressure wave exits the tube. That's like a reverse-phase pressure pulse. The pulse travels back down the tube, reflects and arrives back at the mouth delayed by the time of flight. If that down and back time is 1/2 wavelength (tube is 1/4 wavelength long) it arrives back at the mouth in phase with the original and reinforces it. If it's a bit off the quarter wave F, you still get reinforcement but less of it -- just like you measure when you put a mic up to a port.

[MJKing]

Yeah, Martin what's 3 or 4 inches of length on a 30 inch pipe anyway? We'll just put that one in the equation fudge factor and mark it as the "K" constant....
:rofl:

Lets do the math.

L = c / 4 x 109 Hz = 30.972 in

or

L = c / 4 x 100 Hz = 33.760 in

delta L = 2.788 inches which is a little less than "3 to 4 inches".

Assuming an end correction, similar to what is applied for a port in a bass reflex box to represent the extra length that models the mass term in the acoustic impedance boundary condition at low frequencies, you can back calculate the approximate radius of Augspurger's pipe.

2.788 in / 0.60 = 4.647 in

or

2.788 in / 0.85 = 3.280 in

depending on the baffle conditions at the open end of the pipe. You can find these relationships in Beranek's text Acoustics on pages 118 and 122 respectively, near the top of each page. So I would guess that Augspurger used a 6" to 10" diameter pipe to test his driver, seems very reasonable to me.

No fudge factor involved, just basic acoustic theory and physics.

[MJKing]

My simplistic way of looking at the quarter wave thing is there's a pressure decrease when the pressure wave exits the tube. That's like a reverse-phase pressure pulse. The pulse travels back down the tube, reflects and arrives back at the mouth delayed by the time of flight. If that down and back time is 1/2 wavelength (tube is 1/4 wavelength long) it arrives back at the mouth in phase with the original and reinforces it. If it's a bit off the quarter wave F, you still get reinforcement but less of it -- just like you measure when you put a mic up to a port.

That is a good way of explaining what is going on at the fundamental resonance, and near the resonance, for a pipe closed at oine end and open at the other like a TL. After a couple of reflection cycles, the reinforcement can be very high if no fiber damping is used.

Thanks for the input,

[ch83575]

For your information, the young man advising me to read physics 117 got it wrong. An open ended pipe cannot resonate at frequencies corresponding to 3/4 of the pipes length - that would put a node where an anti node belongs.

Please re-read my post. The second resonance has a wavelength of 4/3 the pipe length which is to say the length of the pipe is 3/4 the wavelength:



Just for the record I am 30 and this is my second degree. I hope that still qualifies me as young, unfortunately I think that once you wish you were younger instead of older you have crossed some invisible line into the beginnings of oldness.

It is an interesting discussion if you can ignore villastrangiato's attitude. A lot can actually be learned from this post if you read it carefully and don't let yourself get worked up too much.

I should probably get back to studying for physics 2 :roll:

-Chad

[MJKing]

Just for the record I am 30 and this is my second degree. I hope that still qualifies me as young, unfortunately I think that once you wish you were younger instead of older you have crossed some invisible line into the beginnings of oldness.

Yup, you are still young (but a little older then I thought). I guess my Dad is probably old, I am in the middle someplace.

Second degree, good for you.

TLs are interesting speaker designs, been thinking about them for over 20 years. Learn something new with every one I design or build.

[villastrangiato]

Please re-read my post. The second resonance has a wavelength of 4/3 the pipe length which is to say the length of the pipe is 3/4 the wavelength:



Just for the record I am 30 and this is my second degree. I hope that still qualifies me as young, unfortunately I think that once you wish you were younger instead of older you have crossed some invisible line into the beginnings of oldness.

It is an interesting discussion if you can ignore villastrangiato's attitude. A lot can actually be learned from this post if you read it carefully and don't let yourself get worked up too much.

I should probably get back to studying for physics 2 :roll:

-Chad

Chad, could you explain to me what the magnitude of a sinusoid would be at the distance in time corresponding to three quarter's of it's wavelength? If you are talking about standing waves in a pipe with one end open and the other closed - the anti- node being at the open end, doesn't that by definition mean the value of the sinusoidal wave cannot be anything other than 0 at the open end? Maybe I'm missing something - I know, I can be stupid sometimes, we all have our moments - please explain how a "standing wave" in a pipe with one end closed and one end open can have it's peak value (270 degrees phase) at the pipe opening. (this should be interesting :rofl: )

A resonant standing wave of 4/3 the pipe length is 1 and 1/3 how do you get a null at 120 degrees phase?

If you look at the lower diagram my friend, you will see that the hand written wave has a peak value at the open end - a physical impossibility when describing an anti node standing wave. Yes, I think you do need to go back to class. The value of the magnitude of the sinusoid standing wave in such a pipe, by definition, must be zero at the output - not maximal. Placing two waves in the picture is a clever way to confuse people - neither of them are standing waves - try using this on someone else to fool them - I'm not buying.

[ch83575]

Chad, could you explain to me what the magnitude of a sinusoid would be at the distance in time corresponding to three quarter's of it's wavelength? If you are talking about standing waves in a pipe with one end open and the other closed - the anti- node being at the open end, doesn't that by definition mean the value of the sinusoidal wave cannot be anything other than 0 at the open end? Maybe I'm missing something - I know, I can be stupid sometimes, we all have our moments - please explain how a "standing wave" in a pipe with one end closed and one end open can have it's peak value (270 degrees phase) at the pipe opening. (this should be interesting :rofl: )

I am not positive, but I feel like you are trying to mock me. Do you really need me to explain the principals of constructive interference that are responsible for standing waves? If so, I do not think you have any right to be using that tone.

-Chad

[MJKing]

Chad has plotted the air velocity profile. The axial air velocity is always zero at the closed end and cycles between positive and negative maximum values at the open end. This means the air moves in and out with maximum travel at the pipes open end for the first standing wave. The pressure profile is the opposite, it cycles through a positive and negative maximum at the closed end and is always zero at the open end.

If you read my TL anatomy article all of this is explained and plotted. The wave equation is solved closed form to show these simplifed motions and then with the real acoustic boundary condition applied at the open end.

[villastrangiato]

Chad has plotted the air velocity profile. The axial air velocity is always zero at the closed end and cycles between positive and negative maximum values at the open end. This means the air moves in and out with maximum travel at the pipes open end for the first standing wave. The pressure profile is the opposite, it cycles through a positive and negative maximum at the closed end and is always zero at the open end.

If you read my TL anatomy article all of this is explained and plotted. The wave equation is solved closed form to show these simplifed motions and then with the real acoustic boundary condition applied at the open end.

Air velocity profile? You're joking, right? Sound is a wave of air pressure. In a pipe with one end open and the other end closed off by a transducer - the peak pressure starts at the transducer and travels towards the open end. The sinusoidal pattern doesn't represent velocity - it represents changes in pressure. The wavefront's velocity is constant - what planet are you from - or better yet, what school did you go to?

[villastrangiato]

An anti node is defined as a place of null or minimal disturbance that occurs when the measured pressure along a vibrating air column is constant and generally in equilibrium with the surrounding environment's pressure. Do you have a problem with this definition Chad? If so, please share your definition in the context of a pipe with one open end and the other sealed by a transducer that excites the pipe.

[ch83575]

If you look at the lower diagram my friend, you will see that the hand written wave has a peak value at the open end - a physical impossibility when describing an anti node standing wave. Yes, I think you do need to go back to class. The value of the magnitude of the sinusoid standing wave in such a pipe, by definition, must be zero at the output - not maximal. Placing two waves in the picture is a clever way to confuse people - neither of them are standing waves - try using this on someone else to fool them - I'm not buying.

First, if you have more to say, do it in another post. Please don't just edit your old posts to add more insults.

Second, I am not making this stuff up:



This is from my physics textbook (its a good thing I really am studying physics right now!). I just held it up in front of the camera in my laptop, so not a lot of detail. It is specifically describing a pipe being excited from the open end by a tuning fork. I am not entirely confident that it is exactly the same when excited from the closed end (or somewhere along the pipe), I leave that to more capable hands.

Martin:
Thanks for the encouragement... I need all I can get! Turns out a degree in architecture is only one (small) step up from a BFA - sorry to all those BFAs round here.

-Chad

[MJKing]

Air velocity profile? You're joking, right? Sound is a wave of air pressure. In a pipe with one end open and the other end closed off by a transducer - the peak pressure starts at the transducer and travels towards the open end. The sinusoidal pattern doesn't represent velocity - it represents changes in pressure. The wavefront's velocity is constant - what planet are you from - or better yet, what school did you go to?

For a pressure wave to progress along the pipe, molecules of air have to move back and forth to compress and decompress the air locally as the pressure wave passes. What is shown in the plot is the relative magnitude of the air velocities oscillating back and forth with no net motion or flow of air. On my site you will find both the oscillating velocity and the pressure profiles plotted.

Every post you make shows how little you understand. I have a BS from Union College and an MS from RPI both in Mechanical Engineering with concentrations in dynamics and vibration. Couple those degrees with over 30 years in various analytical engineering positions (no time wasted in management) doing vibration analysis and testing. All of the speaker design theory is self taught. That is the planet I am coming from.

I am amazed that the moderators on this site tolerate your posting style, it is a poor reflection on the site in general.

[villastrangiato]

I am not positive, but I feel like you are trying to mock me. Do you really need me to explain the principals of constructive interference that are responsible for standing waves? If so, I do not think you have any right to be using that tone.

-Chad

Nope, but I feel the need to inform you that all test data and all texts on this subject conclusively state that anti nodes occur at even multiples of the fundamental of a resonant mode and any multiple of 1/3 is not an "even" multiple in the school I went to.

[villastrangiato]

For a pressure wave to progress along the pipe, molecules of air have to move back and forth to compress and decompress the air locally as the pressure wave passes. What is shown in the plot is the relative magnitude of the air velocities oscillating back and forth with no net motion or flow of air. On my site you will find both the oscillating velocity and the pressure profiles plotted.

Every post you make shows how little you understand. I have a BS from Union College and an MS from RPI both in Mechanical Engineering with concentrations in dynamics and vibration. Couple those degrees with over 30 years in various analytical engineering positions (no time wasted in management) doing vibration analysis and testing. All of the speaker design theory is self taught. That is the planet I am coming from.

I am amazed that the moderators on this site tolerate your posting style, it is a poor reflection on the site in general.

Martin, no one is saying molecules are transferred - your hyper explanation designed to confuse is completely irrelevant to the matter at hand. An anti-node is a point of minimal energy relative to the environment. The reflective node is a point of peak energy (the diaphragm is considered a peak or reflective node in this example). So let's stop trying to turn the world upside down with discussions about velocity. Anyone with a sixth grade education will tell you that sound energy travels at an essentially constant rate. Does it matter how fast the molecules vibrate in their places - not for this discussion - unless your intent is to sidetrack and attempt to impress others with your knowledge of useless information.

[ch83575]

Martin, no one is saying molecules are transferred - your hyper explanation designed to confuse is completely irrelevant to the matter at hand. An anti-node is a point of minimal energy relative to the environment. The reflective node is a point of peak energy (the diaphragm is considered a peak or reflective node in this example). So let's stop trying to turn the world upside down with discussions about velocity. Anyone with a sixth grade education will tell you that sound energy travels at an essentially constant rate. Does it matter how fast the molecules vibrate in their places - not for this discussion - unless your intent is to sidetrack and attempt to impress others with your knowledge of useless information.

Allright... I'm done. This one actually made me spit the coffee I am drinking on my computer. I am having trouble typing through my laughing fit. If this "villastrangiato" dude is some kind of joke, its a good one.

-Chad

[villastrangiato]

Once again, anyone interested in participating in a serious discussion about Mr. Augspurger's paper or TL's in general should read the subject matter carefully before adding their two cents as if they understand physics and the person(s) who started this thread are totally ignorant. The test under discussion was performed by George Augspurger. If you would care to read it, it would tell you a transducer was placed at one end of a pipe, the other end was open. Not one end closed and the other with a transducer placed on it. I don't care what school you go to, or how many degrees you have, if you're going to barge into a serious thread and start insulting people, the least you could do is find out what the people are talking about - doing otherwise is JUST PLAIN RUDE.

[Dennis H]

Please re-read my post. The second resonance has a wavelength of 4/3 the pipe length which is to say the length of the pipe is 3/4 the wavelength:

Exactly, Chad. Per my simplistic example above, the so-called reflection at the open mouth is caused by a pressure decrease as the wave expands into open air so it has inverted polarity. To travel down the pipe and arrive back at the mouth in phase, it has to travel 0.5, 1.5, 2.5, etc. wavelengths. The pipe length is half that or 1/4, 3/4, 5/4, etc. wavelengths. At lengths of 2/4, 4/4, 6/4, etc. you get dips as the reflections arrive back at the mouth out of phase. That's where stuffing the line comes in -- let the low stuff through and filter out the higher frequency peaks and dips.

[villastrangiato]

I am amazed that the moderators on this site tolerate your posting style, it is a poor reflection on the site in general.

Well, dealing with you, I admit, my patience sometimes wears thin. But then, my posting style doesn't include barging into threads telling people they need to delete a university professor's published paper from their hard drives because it doesn't square exactly with my opinion - "because I've done all the calculations". No Martin, you bring rudeness to a whole new level.

[Dennis H]

If you would care to read it, it would tell you a transducer was placed at one end of a pipe, the other end was open. Not one end closed and the other with a transducer placed on it.

Well, trying to be polite about it, I think we all know that.

I only see one person in this thread being rude and not understanding what others are saying.

[villastrangiato]

Exactly, Chad. Per my simplistic example above, the so-called reflection at the open mouth is caused by a pressure decrease as the wave expands into open air so it has inverted polarity. To travel down the pipe and arrive back at the mouth in phase, it has to travel 0.5, 1.5, 2.5, etc. wavelengths. The pipe length is half that or 1/4, 3/4, 5/4, etc. wavelengths. At lengths of 2/4, 4/4, 6/4, etc. you get dips as the reflections arrive back at the mouth out of phase. That's where stuffing the line comes in -- let the low stuff through and filter out the higher frequency peaks and dips.

Actually Dennis, I'm glad we had this discussion. The quote above is going to get framed and put on the wall of my office. Your "wave expands into open air so it has inverted polarity" will be a great conversation piece!!! :rofl:

[Dennis H]

We always seek to be entertaining. Who knew basic high school physics would be so hard to understand and such a source of laughter? Have fun displaying your ignorance to your friends if you have any. (Here comes Thomas with the padlock)

[ThomasW]

We always seek to be entertaining. Who knew basic high school physics would be so hard to understand and such a source of laughter? Have fun displaying your ignorance to your friends if you have any. (Here comes Thomas with the padlock)

Yeap