TL Facts
Stuffing does indeed make the line effectively longer. A TL has distributed mass, compliance, and resistance per unit length of the line, stuffing increases the compliance due to moving the system from adiabatic closer to isothermal conditions. The line appears longer when the compliance is increased:
Isothermal and adiabatic expansion
It can be seen here that the speed of sound is dependent on the adiabatic constant. The speed of sound does change due to the change in compliance:
Speed of Sound
I've actually seen several researchers who do not know how to find the l/4 frequency; it is the minimum in input impedance between the two lowest peaks in the impedance curve and it is the lowest freq minimum in the driver cone displacement. It is dependent on the line and not driver characteristics.
These are basic fundamentals.
Stuffing does indeed make the line effectively longer. A TL has distributed mass, compliance, and resistance per unit length of the line, stuffing increases the compliance due to moving the system from adiabatic closer to isothermal conditions. The line appears longer when the compliance is increased:
Isothermal and adiabatic expansion
It can be seen here that the speed of sound is dependent on the adiabatic constant. The speed of sound does change due to the change in compliance:
Speed of Sound
I've actually seen several researchers who do not know how to find the l/4 frequency; it is the minimum in input impedance between the two lowest peaks in the impedance curve and it is the lowest freq minimum in the driver cone displacement. It is dependent on the line and not driver characteristics.
These are basic fundamentals.
Last edited:
If one considers TL loading on driver, one will likely see that adding stuffing may vary the loading as shown in the impedance curves; but does this effect the wave length the same way? I do not think so. It does effect damping.
I understand pretty much the effects of isothermal and adiabatic conditions but if the effective line length is increased from stuffing it, and I still don't think it is but I won't debate it with you, how large is this effect? 1%, 10%, 50%, or what? My memory says people were expecting to be able to shorten a required line length by siginficant amounts, but the results weren't as they expected.
Paul
Paul
So, adding stuffing makes the effective line length ~18% longer? Does it matter what the stuffing density is and/or how much of the line's length is stuffed?
My direct experience with adiabatic/isothermal conditions came from observing the shape, rise time and settling time of a pressure waveform in a closed container as the thermal condition was adjusted from adiabatic to isothermal. The thermal condition was adjusted by adding copper foil "sponges" to essentially absorb the temperature increase that occurs when a slug of pressure was injected. Without any copper, the pressure rose rapidly, overshot, and had a few cycles of "ringing" before settling to its steady-state level of thermal equilibrium. As copper was added, the rise time began to increase while overshoot and ringing lessened, until after enough copper was added, there was neither overshoot nor ringing, indicating an isothermal condition had been established. Adding more copper after that did nothing more other than consume volume. Therefore, if there is a line-lengthening effect caused by adding stuffing to a TL, I would suspect it would be far less than 18%. And, whatever effect it would have I also suspect it would be very specific, like a very specific density over a very specific length.
Paul
My direct experience with adiabatic/isothermal conditions came from observing the shape, rise time and settling time of a pressure waveform in a closed container as the thermal condition was adjusted from adiabatic to isothermal. The thermal condition was adjusted by adding copper foil "sponges" to essentially absorb the temperature increase that occurs when a slug of pressure was injected. Without any copper, the pressure rose rapidly, overshot, and had a few cycles of "ringing" before settling to its steady-state level of thermal equilibrium. As copper was added, the rise time began to increase while overshoot and ringing lessened, until after enough copper was added, there was neither overshoot nor ringing, indicating an isothermal condition had been established. Adding more copper after that did nothing more other than consume volume. Therefore, if there is a line-lengthening effect caused by adding stuffing to a TL, I would suspect it would be far less than 18%. And, whatever effect it would have I also suspect it would be very specific, like a very specific density over a very specific length.
Paul
Last edited:
And the 18% figure assumes ideal best case. Only the air that has good heat flow to the stuffing moves to isothermal behavior, so if you just lined the walls the effect would be much smaller. There is an optimum density from the point of view of making the line behave longer, however it might not also be the best case for line damping.
Also, damping near the port end of the line is analogous to lowering Qp in a vented system which we usually do not want to do. Stuffing towared the driver end is analogous to lower Qb and is where more stuffing should be used.
pkitt: You seem curious, and MJK has some excellent test data, however I disagree with his interpretation. Without reading MJK's analysis, where do you think the l/4 frequency is in his Figure 2.2 in his paper:
http://www.quarter-wave.com/TLs/Test_Line_Results.pdf
I'll help with the interpretation and if you are interested you can compute how close it gets to the 18% figure.
Let me offer one point; the input impedance of an open ended TL at the l/4 frequency is an acoustical short (ideally for infinite Q)
from a volume velocity perspective. In other words the cone displacement goes to zero (ideally) as it does at Fb in a vented system.
Note that the vented system box and port form a series resonant system.
http://www.quarter-wave.com/TLs/Test_Line_Results.pdf
I'll help with the interpretation and if you are interested you can compute how close it gets to the 18% figure.
Let me offer one point; the input impedance of an open ended TL at the l/4 frequency is an acoustical short (ideally for infinite Q)
from a volume velocity perspective. In other words the cone displacement goes to zero (ideally) as it does at Fb in a vented system.
Note that the vented system box and port form a series resonant system.
Last edited:
His measurements showed a reduction of about 3.4% in the speed of sound for a packing density of 1 lb / cu ft in the pipe.
The testing methodology doesn't look brilliant (to me) but I thought I'd mention it anyway as the subject had cropped up earlier in this thread, but I didn't recall seeing any kind of tests confirming the claims one way or the other.
Are you a thermodynamics expert? Where did you do this experiment? What did you use as a pressure transducer?
No, I'm not a thermodynamics expert. Are you? I'm a retired BSEE if you have to know in order for my comments to have some credibility with you. The "experiment" I described was just one of the many things I did during my 40-year career in designing, manufacturing, testing, quality-controlling and acquiring regulatory approval of electronic and electromechanical medical devices. The specifics of that experiment were directed towards creating calibrated, isothermal "lungs" which were then used to accurately measure the performance of ventilators we manufactured.
Paul
Paul
If guesses from the peanut gallery are welcome, I'd say a little under 65Hz, where the electrical impedance phase crosses through zero.
That's easier for crusty old eyes to see than trying to pick an exact minimum from the impedance magnitude plot.
A quick look at the high frequency end of the graphs to get an idea of voice coil inductance suggests that that won't be too significant at the frequency of interest.
The guess above is also supported by a quick sanity-check with simple theory, which suggests L/4 resonance at about 70Hz for L=4ft (ignoring end correction).
Just trying to get some perspective in order to know where you're coming from.
No, I am not a thermo expert but my father is, so I got a lot of lectures anytime I asked a question about thermo problems over the years.
That's interesting, i'm assuming the same kind of thing applies to volume reduction in a sealed box to obtain the same resonance frequency. That tallies very well with what i find with stuffed boxes at any rate, i manage somewhere about the figure of 18% volume reduction stuffing with rockwool.
In fact i got better results with rockwool than supposedly superior long hair wool 😕
Interesting thread, i have been following it but that figure made me comment simply because it is believable.
Yes that was my figure also, and you're right the VC inductance introduces an error term but it should be very small as you noted.
He lists the computed l/4 as 67 Hz in Table 2.2 so the agreement is excellent.
And we should note the amplitude of the minimum as compared to Re which represents how close to an ideal short the line is. It is similar to blocking the cone so that the mechanical impedance is not reflected into the primary.
I just wanted to mention that thermal effects are not the only way that the speed of sound can be slowed. It may not even be the most significant. When there is a matrix of porus solid medium within the pipe then there is a path length increase and this slows the wave as far as the bulk motion is concerned. This is precisely how light waves are slowed in a refractive medium, since we know that the speed of the wave at any instant isn't actually slowed, because that's impossible.
Rockwool and dacron fibres are much smaller in diameter than wool fibres. The effect of this was covered in one of the papers that discussed whether the speed of sound was actually slowed by stuffing. I'll see if I can find it.
- Status
- Not open for further replies.