Speed of sound in a tube

I've been told that Goubau lines were popular for use in mine communications until leaky coax became readily obtainable and cheap.

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Hey the tunnel is perhaps too big!

The cutoff is at wavelength equal to twice the diameter.

1kHz is about 30cm, D =3D 15 cm... 100 Hz D =3D 1.5M 10Hz 15m

Small culverts are a perfect size.

No worries with small pipes.

George H.

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The coax was not a 'perfect' analogy. I'm not smart enough to figure out the differences without a lot of time... But there must be some modes with a node down the center.

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Acoustics is still the wave equation. I'll have to go look up how it all relates,

A spherical resonator has solutions that are spherical harmonics. Hydrogen atom RF cavity Acoustical resonator.

It's all the same.... mostly.

George H.

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dcaster@munged_address_krl.org Mon, Mar 19, 2012 at 3:30 PM To: Robert Macy

Dan,

Thanks for the 'heads up' 109 was a typo and got left in.

I am not familiar with Kaye and Laby, and a search turned up no acoustics book, what is the title?

I posted some relevant book excerpts on ABSE for you.

I am not buying any speed difference for the case of a perpendicular sound wave traveling straight down the tube. A sound wave entering the tube at an angle will bounce off the sides of the tube, with a longer path length, and an apparent decrease in sound speed due to the increased path length - but no real change in the speed. The case of the round tube, where different parts of an oblique plane wave get reflected in different directions, seems like it could only be solved with a good finite element model.

Electrical analogies are not entirely inappropriate; there is a reflection from the impedance discontinuity at the ends of the tubes just like the reflections from impedance discontinuities in a transmission line, but the wave equations for sound in an ideal gas are much different than for EM fields, being inherently nonlinear and having no closed form solution. Blackstock does a really good job of explaining this IMO, both in the previously mentioned book and in 'Nonlinear Acoustics' by Hamilton and Blackstock. Instantaneous sound pressure at a point, unlike electrical or magnetic fields, is a purely scalar value, not a vector, and has the nonlinear influence of compression heating and expansion cooling, with speed being a function of temperature.

The edge effects of sound in a tube are quite interesting too. You might expect that since air motion in a plane sound wave traveling straight down the tube is in a straight line parallel to the tube with no turbulence, similar to laminar flow, that the amplitude (ac flow) profile across the tube would be similar to a laminar flow profile, but it is not, it is much more like a turbulent flow profile with a slight quirk:

distance from tube wall - vertical axis | | | |

It's not actually a book on acoustics, but it is the first place to look for basic information about physical properties: "Tables of Physical and Chemical Constants"

I believe there is an online version.

Thanks. I don't seem to be able to get that group on my server, but I am looking for alternative ways to view it.

I was once involved in an experiment to track a sound pulse (from a spark generator) as it travelled down a recording horn. The results were so complicated that we never made sense of them.

It sounds as though I have opened a real can of worms here. However, most of the effects you have described will either have no practical effect on my prototype design or may even be slightly beneficial - so that was the answer I was looking for.

--
~ Adrian Tuddenham ~
(Remove the ".invalid"s and add ".co.uk" to reply)
www.poppyrecords.co.uk

I am sure that the CRC Handbook of Chemistry and Physics would have quite a few relevant tables as well.

Thanks.

I will email them to you.

I believe it. I once took data on a spark generated shock wave experiment, and we were very careful that no reflection could reach the microphone before we were done taking data - the reflections looked a lot like white noise, which seems to make sense considering that the N wave produced by a spark has frequency content extending from probably low audio (never looked at that end) to at least 2 MHz, the limit of our microphone. I would be inclined to characterize a horn with a swept sine wave, although an FFT of the multiple echo hash you get from an N wave might reveal something about frequency response.

munged by line wrap first try:

distance from tube wall - vertical axis | | | | > with a flat profile in the middle of the tube. tapering to zero at the

Wow, how did anyone ever get to the moon without a finite-element model? ;)

Unless the tube diameter is larger than 1.22 wavelengths (first null of J1(2*pi*r/lambda), only the lowest-order mode can propagate, so once you get more than a couple of diameters away from the open end, you're strictly in the axial-propagation case.

The evanescent modes can influence the overall phase shift, which is one way of looking at the end effect.

Cheers

Phil Hobbs

--
Dr Philip C D Hobbs
Principal Consultant
ElectroOptical Innovations LLC
Optics, Electro-optics, Photonics, Analog Electronics

160 North State Road #203
Briarcliff Manor NY 10510
845-480-2058

hobbs at electrooptical dot net
http://electrooptical.net

Wow, great example :-). Those lamers had such poor analytical skills that they had to blow 2 million of our tax dollars writing NASTRAN, which was then then distributed to every engineering school in the country for the cost of reproduction, indoctrinating an entire generation of engineers in reliance on the evil crutch of FEA. Almost as bad as that nasty SPICE and EM field solver stuff :-).

Today NASA would turn such a taxpayer funded development over to their legal department for licensing to the highest bidder, so you needn't worry about a repeat of that fiasco :-).

I'll buy that, but I must admit to being too dense to see how to go from that approximation to a decent model of the line microphone. Since the prime weakness of this design is loss of directionality with decreasing frequency, causing a nasty frequency dependency for off axis sources, a decent model needs to predict how directionality vs frequency changes with the various design modifications under consideration. Though I seem to have moved a bit beyond the thread subject there, and admit a moon landing level of effort might not quite be justified :-).

Nastran wasn't in use in NASA before 1968, at least according to Wiki. I sort of gather that most of the design work had already been done by then. Do you know of any parts of Apollo it was used on in the design phase?

And relying on simulation for simple stuff like a tube is a strong sign of a one-trick pony.

Cheers

Phil Hobbs

--
Dr Philip C D Hobbs
Principal Consultant
ElectroOptical Innovations LLC
Optics, Electro-optics, Photonics, Analog Electronics

160 North State Road #203
Briarcliff Manor NY 10510
845-480-2058

hobbs at electrooptical dot net
http://electrooptical.net

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Hi Phil, According the the paper I read, the cut-off is at lamda =3D 2D/1.172... It's the zero of the other Bessel function.

I'll send you a copy on Monday. I was also recording some sound files with my son... We've got both a 30" and 18" conduit under our road.

The recordings sounded kinda poor... so no promises. But it's always nice to have some real data.

George H.

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Hi, George,

It needs to be at an antinode of J0, which is a null of J1, unless I'm missing something ultra-important (which is always a good possibility). The lowest order peak is at 0, and the next one is at

3.83 and change, so with a factor of 2*pi for the propagation factor and 1/2 to go from diameter to radius, that's ~1.22. What did the paper say it was?

Cheers

Phil Hobbs

--
Dr Philip C D Hobbs
Principal Consultant
ElectroOptical Innovations LLC
Optics, Electro-optics, Photonics, Analog Electronics

160 North State Road #203
Briarcliff Manor NY 10510
845-480-2058

hobbs at electrooptical dot net
http://electrooptical.net

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Grin.. Late Saturday, after watching my hockey team* win again. I'll send you a copy of the paper on Monday and you can tell me. It's a fun read and perhaps can tweak your understanding a bit.. Either that or you can correct me.

George H.

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Well, probably we can all learn something, which is always good news.

My recollection, from the days of entering element nodes, restraints and loads with punched cards, was that Nastran was developed specifically to solve the pogo issue with the Saturn V used for Apollo, so no, it was not used in the initial design stages, just to fix a serious problem in the design afterwards, but used before any actual moon landing IIRC. Public release was some time later, perhaps '68.

Not that I am opposed to analysis, but it is of limited use if the wrong question is asked. The right question is, what is the directionality vs frequency, not easy even for a single tube coupled to a microphone in a chamber beyond the end of the tube, and well beyond any reasonable hope of accurate analysis for the entire multi-tube assembly IMO. FEA with an acoustic field solver could, on the other hand, be set up with a parametric design and optimized for least variation in directionality with frequency while keeping on-axis frequency response within some limits, for example. Try that with pencil and paper!

Sure, we're in violent agreement about the usefulness of simulations once the complexity level gets too high. I spent about a year of my life writing an optimizing fullwave electromagnetic simulator do design infrared antennas with, because I couldn't buy one at the time.

But that wasn't what my original comment was about--we were discussing propagation with a single small-diameter tube, where the solution is pretty simple. Mode-matching the incident wave isn't that hard either, in such a simple geometry. (Geometries where the Laplacian doesn't separate are considerably tougher analytically, and of course those are in the great majority.)

Cheers

Phil Hobbs

--
Dr Philip C D Hobbs
Principal Consultant
ElectroOptical Innovations LLC
Optics, Electro-optics, Photonics, Analog Electronics

160 North State Road #203
Briarcliff Manor NY 10510
845-480-2058

hobbs at electrooptical dot net
http://electrooptical.net

We are also in complete agreement that an exact solution is always preferable, where it exists. Very useful for validating your finite element solver, and I hear sometimes even applicable to real problems. But, what exact solution were you referring to? All I can find is this:

And I have to reject this as an exact solution, as your assumption of mode shape is not even close to measured reality, which I attempted to show with ascii art with dismal results, so I will just describe the actual observed longitudinal wave propagation mode. Many smart people were once expecting the mode you described, when it was observed that amplitude (pressure or displacement) was constant across the majority of the center of a tube, with the edge effects including a small peak just before the near linear taper to zero at the tube wall.

A useful approximation can be made by neglecting nonlinear effects and losses. The no loss assumption of course does not model the edge effects well and the linear assumption limits usefulness to sound pressures well below atmospheric, but these effects can be shown to be small for many useful geometries, and with this approximation an exact solution has been found for rectangular waveguides (see Blackstock for instance), but I am not currently aware of an exact solution for round acoustic waveguides which can be used to accurately model entry effects as a function of angle of incidence. Not that my knowledge of the subject is anywhere near complete, I could well be wrong about that exact solution but I don't really have time to pursue it at the moment.

Regards, Glen