Does the speed of sound change? Opinions...

[purplepeople]

Hi all,

This has been moved from another thread to prevent a hijacking.

:)ensen.


I wrote:

... I think that adding stuffing to "slow the speed of sound" and "make the line longer" are refering to the same thing, which is that it takes more time for a wave originating at the driver to make its way to the open end of the transmission line.

Physics has proven (to me) beyond most reasonable doubt that the speed of sound in air is dependent on pressure and temperature and remains the same if those two values don't change. It is faster in denser fluids like water and faster still in solids like steel. It does not slow when it hits the stuffing, but it does follow the contours of the surface of the stuffing which forces the wave to zig and zag over a greater distance. The line is not longer, but the travel distance is. The speed of sound is not slower, but it takes more time for the wave to hit the opening.

Wavelength has a role to play here. If you choose a stuffing with extremely rough surface elements - say tennis balls - they will also lower frequencies than stuffing that is finer, like Velcro. This is why most stuffing like wool will attenuate high frequencies but not work on bass notes. In addition to damping the energy in the wave, it forces small wavelengths to travel along the surface irregularities making them take "forever" to reach the opening of the line. If you look at the egg-crate stuffing used by PMC,

(http://www.pmcloudspeaker.com/transmission.html)

it will not only attenuate higher frequencies because of the open-cell foam material being used, but will also make some of the lower frequences travel a longer distance, increasing the "effective" line length as stated in their specs.

[purplepeople]

And here was the response from MJK....

:)ensen.

Physics has proven (to me) beyond most reasonable doubt that the speed of sound in air is dependent on pressure and temperature and remains the same if those two values don't change. It is faster in denser fluids like water and faster still in solids like steel. It does not slow when it hits the stuffing, but it does follow the contours of the surface of the stuffing which forces the wave to zig and zag over a greater distance. The line is not longer, but the travel distance is. The speed of sound is not slower, but it takes more time for the wave to hit the opening.

I am not sure I agree with this reasoning for the reduced speed of sound in a fiber filled pipe. Remember that a sound wave traveling down a pipe is really small back and forth motions of air at any given location. These motions act like a falling chain of dominos as the sound wave travels along the length. A particular molecule of air does not really move very far and returns to its original postion after the wave has passed.

I think that the slight slowing of the speed of sound in a fiber filled TL is due to the loss of the perfectly adiabatic expansion and compression of the air as the sound wave passes. As the air is compressed it increases in temperatue slightly and some heat is transfered to the fiber. When it expands it drops in temperature and the now warmed fibers give the heat back to the air. This is the same as what happens in a closed box when it appears to have a larger volume when fiber filling is added.

If you buy my hypothesis, the the absolute lower limit for the speed of sound is calculated as follows :

c' = c (1.0/1.4)^0.5 = 0.8452 c

This represents the transition from an adiabatic process to an isothermal process. In reality, I doubt that this lower limit can be achieved and more then likely the lower limit is closer to the following :

c' = c (1.2/1.4)^0.5 = 0.9258 c

When a sound wave, that is at least four times longer then the length of the pipe, encounters a fiber that is that small I think that the wave just passes around the fiber as if it were not there. Remember that shear stresses are not present in air so I do not see the sound wave "bending" as it wraps around an object.

[purplepeople]

I just realized that the speed of sound is different than the speed of the moving air...

When an amp excites a driver, the voice coil and cone move a column of air the distance of the excursion. Let's say the driver has a peak to peak excursion of 1 mm. At 1 Hz, the voice coil has an average physical speed of 2mm/sec. It follows that 1000 Hz gives a speed of 2000mm/sec and 20KHz gives a speed of 40000mm/sec. These are all significantly slower than the speed of sound at standard temperature and pressure (STP) which is ~ 340 m/s = 340000 mm/sec.

(As an aside, it is interesting to note that a tweeter with 10 mm excursion at 20KHz would give an average coil speed of 400 m/s. Would this cause a sonic boom?)

While I agree with Martin that heat energy is involved, I only believe it is related to the law of conservation of energy so that a sound wave does not travel forever. The apparent increase in box volume is merely a lowering of resonances and only because we can't actually hear all of them. All the resonances are still there, just attenuated due to heat loss in the stuffing as you describe.

The compressiblity of air is what makes the speed of sound constant at any given temp and pressure. If we were to chop up the enclosure into infinitesimally small slices, we'd find that as there is a time lag between when the driver moves and when the air at the end of the first slice moves. It's like a Slinky(c). You pull/push on one end and the wave takes time to travel to the other end. This is why sound does not travel in a vacuum and why it is faster in denser materials like liquids and (homogeneous) solids.


:)ensen.

[Bill Fitzpatrick]

If you would, take a few posts to address the following related question.

Let's say you stretch a sufficient number of layers of cloth in front of a tweeter to cause a high frequency roll-off.

The question is:

Is the roll-off accompanied by a phase shift as it would be when you put a small inductor in series with the tweeter?

[SY]

A rolloff is a rolloff is a rolloff. The cloth will still be minimum phase, so you'll get exactly the same phase behavior as rolling off the tweeter electrically.

[planet10]

Originally posted by purplepeople
a tweeter with 10 mm excursion

That would be quite a tweeter...

dave

[Pjotr]

And consider what a IM (and/or Doppler) distortion such a huge excursion will cause with tweeters, even if the tweeter itself is perfectly without any distortion.

[purplepeople]

So, it cloth in front of a driver causes a phase shift, wouldn't stuffing do the same, even if only along the inside surface and not covering the cross-section. Stuffing must do this or else there would be a doppler shift in the freqency and a corresponding lengthening of the wavelength. Or is the lowering of the fundamental the same doppler that Pjotr is speaking of? Hmmm...

Plus, you guys got me thinking about that tweeter or something like it. And the only thing I though of is normally measured by its calibre, as in .45 caliber, 9mm or 12 gauge. And yes, I believe they create a sonic boom. And yes, cloth, stuffing or probably even 5/8" MDF won't really cause a phase shift here.

:)ensen.

[phase_accurate]

I think the main error lies in the assumption that the sound basically moves through the air between the fibers.

Correct would be to think of the sound propagating through the (more or less) homogeneous medium consisting of air and fibres.

This would raise the possibility of wave-propagation, that is different from the wave-propagation through air, quite a lot.

Regards

Charles

[MJK]

A couple of comments :

purplepeople wrote :

While I agree with Martin that heat energy is involved, I only believe it is related to the law of conservation of energy so that a sound wave does not travel forever. The apparent increase in box volume is merely a lowering of resonances and only because we can't actually hear all of them. All the resonances are still there, just attenuated due to heat loss in the stuffing as you describe

The closed box example has two different things going on.

1) First, at the system resonance, fc = 30 Hz or 40 Hz or 50 Hz, the box internal dimensions are most likely too small to support a half wavelength standing wave. So the compression that takes place inside the box at fc is a simple uniform compression. The heat transfer between the compressed air and the stationary fibers drops the ratio of the specific heats from 1.4 to some smaller value which is probably no lower then 1.2 (can't be lower then 1.0). This is what causes the perceived increase in box volume and a lowering of the system fc.

2) At frequencies high enough to generate standing waves in the enclosure, the fiber provides viscous damping (proportional to air velocity) that strongly attenuates the resonances and improves the speaker's performance. A standing wave in a closed box that has a pressure maximum on the back side of the cone can cause the cone's motion to be significantly reduced producing a sharp dip in the SPL response. For attenuating standing waves, the best place for the fiber is at the points of maximum air velocity which are in the middle of the box and not at the box walls. Lining only the box walls is very inefficient at damping standing waves.


phase_accurate wrote :

I think the main error lies in the assumption that the sound basically moves through the air between the fibers.

Correct would be to think of the sound propagating through the (more or less) homogeneous medium consisting of air and fibres.

This would raise the possibility of wave-propagation, that is different from the wave-propagation through air, quite a lot.

This was the theory originally proposed by Bradbury based on Bailey's TL test results. This was the standard TL fiber model used from the 60's up until recently. The fibers and the air move together at low frequencies producing a greatly reduced speed of sound. At higher frequencies the air decouples and moves independently from the fibers. In one of my theory sections I have a few paragraphs that attempt to explain what I believe fooled Bradbury into proposing this theory.

I initially tried the Bradbury model for several years and could never get correlation between test results and preditions. It just did not work for me or anybody else as far as I know. Several other people, such as Bullock and Augsburger, could not make this model work very well against their own test data. The current thinking is that for small signal responses the fibers do not move and that the fibers only provide viscous damping. For large signal responses, producing large nonlinear cone motion such as the cannons in the Telarc 1812 overture recording, this assumption may not be valid and the fibers being ejected from the open end of a TL are strong evidence of fiber motion. However, for most music at reasonably sane volumes I think the fibers do not move and my assumption's are justified.

In my opinion, there are two things that fibers do to the sound waves in a TL. First, the speed of sound is slightly reduced due to the shift from an adiabatic expansion and compression of the sound wave to a slightly non-adiabatic (not all the way isothermal) expansion and compression of the sound wave as it progresses down the line. Second, the sound wave is attenuated by viscous damping as the velocity of the air passes back and forth throught the fiber tangle. This is the action that attenuates the sound waves of the higher modes. The first quarter wavelength standing wave (1/4) has a velocity maximum at the open end so the minimum attenuation is produced. The higher quarter wavelength modes have velocity maximums inside the line and at the open end so the fibers have a better change to attenuate the standing wave as you go to higher and higher quarter wavelenth modes (3/4, 5/4, 7/4, 9/4, ...). I am not sure if these two effects can be completely separated since viscous damping is probably also generating a small amount of heating of the air.

These are my simplistic hypotheses of the behavior of sound waves in fiber filled transmission lines. They are emperically derived based on the test data I obtained from my test line experiments. I cannot prove them mathematically other then to point out that the MathCad worksheets, based on this theory, correlate very well with the test results as can be seen in the appropriate plots of my Theory Section on my site. There is probably still room for inprovement in my theory but I believe it is good enough right now to confidently design a TL that works as predicted by the MathCad worksheets.

Hope that helps,