# Talk:Speed of sound

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## In Mi/h - Km/h

This article gives equations to find the speed of sound, is there any definite measure of the speed in miles per hour or kilometers per hour? [I used to think it was 1400 mph].

There's a table in Speed_of_sound#Speed_in_airOmegatron 22:58, 20 February 2006 (UTC)
Taking the speed of sound as 340.28 m/s, then it would be very roughly 1225 km/h (rounding to the nearest unit), which would be roughly 761.2 MPH (rounding to the nearest four units).
I came to this page out of curiousity because I read that you can count the seconds between seeing lightning and hearing thunder, then divide by five to see about how far away the lightning was in miles. My guess is that the average person who looks up speed of sound wants to know how fast sound travels in air. I realize that the answer is "it varies - see the equation," but I think the article would benefit from an introduction that says "the speed of sound in air can vary from about X to Y, depending on how hot it is outside, what the humidity is, and your elevation. Underwater, it's more like Z" or something like that. Then you can go into the specifics of sound in various materials and the equations, etc.

--Nathan

It didn't say anywhere about approximately 5 seconds per mile, which I'm sure many people come to the page to find out. I added it to the initial summary. -kslays

A site by NASA gives the speed of sound as 741 MPH

(talkcontribs) 19:01, 2 July 2008 (UTC)

## Terminology

The proper term is "speed of sound", not "velocity of sound." Velocity refers to a vector, but sound is characterized by a scalar: the speed of sound waves in a material, independent of direction. In some materials, sound travels faster in some directions than others, but even in such circumstances it is not characterized (AFAIK) by a vector. -- CYD

This may be correct (as far as velcoity is a vector and speed is a scalar), but is a bit of hair splitting. In Morse's "Theoretical" Acoustics, the index entries for "sound speed" and "sound velocity" are identical. A Scirus search reveals approximately the same number of "sound speed" annd "sound velocity" hits. "Sound velocity" abounds in geophysical literature. So both in technical and other literature velocity is not strictly used for the vectorial quantity. --AMR 22:16, 2004 Nov 5 (UTC)
Please consider that not every book is a bible (even a good one). The term "velocity of sound" is confusing for those who come here to learn and should not not be used. ---TRL 23:25, 2005 Nov 30
The term referring to a vector should not be used when speaking about waves as this phenomenon in general cannot be characterised by the velocity vector. In case of anisothropic materials (materials in which speed of sound does depend on direction) 2nd rank tensor (which may be represented by a square matrix) is used to describe material properties. --Mak Sym 213.134.172.253 18:19, 19 May 2007 (UTC)

## Linear with temperature?

Does anyone have a reference for the claim that speed of sound varies linearly with temperature in air? As far as I know, this is not correct. My "standard atmosphere" table shows it varying strictly with the square root. I believe the linear expression should be removed from the page. -- User:wtph

Not my field, but what you say sounds right. I know for a fact that the speed of sound is higher when the temperature is low - that's why my alarm clock always goes off much earlier on cold winter mornings (especially, for some reason, on Mondays). Tannin 04:30 5 Jun 2003 (UTC)
LOL. But seriously, the speed does vary with √T, and √T is approximately a straight line for the 20°C or so that most people are interested in. I've removed the confused sentence on the origin of the linearity. The rest of the article could still use some editing. -- Tim Starling 04:43 5 Jun 2003 (UTC)
For an ideal gas the speed of sound varies as the square root of (gamma x R x T). gamma is the ratio of specific heats, which for air is 1.403 (dimensionless). R is the specific gas constant which for air is 287 J/kg/K. T is temperature in Kelvin.

To simplify, speed propagates due to the movement of the molecules that make up the gas, and thus speed of sound is proportional to the average speed of the molecules. Temperature is a measure of energy (which is proportional to the square of the velocity). Thus Speed is proportional to square root of energy and thus proportional to square root of temperature. (Understanding this then allows us to determine what effect molecule size will have. Larger molecules have higher mass and thus for the same energy have lower velocity. Thus speed of sound in gases with higher molar mass have lower speed of sound). -- Jon Ayre 14:20 9th Dec 2005 (GMT)

331.5+0.607*T(degrees celsius) meters/second. -- Monohouse 2006

The linear formula commonly used for the speed of sound as a function of temperature is the first-order approximation of the square root formula. In other words, it gives the tangent line approximation to the parabola using zero degrees Celsius as the point of tangency. For temperatures between -40 and 40 degrees Celsius, the linear approximation is within 1 m/s of the square root formula. The errors increase as the temperature gets farther from 0. Richard Hitt Feb 2006

So why don't we include this formula instead of the approximation? It's not that much more difficult...

${\displaystyle c_{\mathrm {air} }=331.5{\sqrt {1+{\frac {\theta }{273.15}}}}}$

Jesse 14:59, 21 June 2006 (UTC)

I've added your equation. The linearized one given before is merely the first two terms of the Taylor expansion of yours. And yours comes from converting the ideal gas one below, which is in Kelvins, to Celsius instead of Kelvin, and collecting all constants but temperature into one (which is the speed at 273.15 K = 0 C). SBHarris 18:06, 11 July 2006 (UTC)
But hang on, this equation cannot be right. This would mean that the value at 0°C equals to
${\displaystyle c_{\mathrm {air} }=331.3{\sqrt {2}}\ \mathrm {m\cdot s^{-1}} }$
Because the fraction equals to 1 and you add 1. Where does this 1 + come from?
I think it should be removed.
--Oderbolz (talk) 19:27, 27 October 2008 (UTC)
The "1+" comes from the conversion from Celsius to Kelvin. The article states clearly that θ is the temperature in Celsius, not Kelvin. At 0°C, θ = 0. I'm removing the "dispute" tag. Spiel496 (talk) 00:25, 29 October 2008 (UTC)
OK, agreed, I should have read more carefully.

--62.167.176.34 (talk) 21:22, 2 November 2008 (UTC)

## Speed of sound = speed of movement of 'pressure'?

Might be stupid, but I was wondering whether the speed of sound actually is the maximum speed that "pressure" can travel through matter. If that is true, we should include it in this article...

Pressure is considered a state variable, so talking about the "speed of movement of pressure" doesn't mean a whole lot. Pressure doesn't "move" from one point to another.

As an explanation to a layman who may not know what a state variable is, one could accurately say the following: if you had a room with totally uniform pressure and then paused time, and you magically increased the pressure at one point in the room and then started time again, that pressure would "travel" at the speed of sound. To be more accurate, one would say that a wave of pressure would travel at the speed of sound.

Far away from the source, if it's a low pressure, yes. The problem is that high pressure waves, such as the hypershock after a bomb detonation, often travel supersonically (like Mach 1.5 at least) for awhile before slowing down to sound velocity. So pure pressure waves can travel supersonically for a time, though there's always a drag and decelleration on them. This shouldn't surprise you: a shock of molecules moving faster than sound isn't going to slow down to sound speed after just ONE hit on the next layer of molecules. Speed of sound formulas assume gentle adiabadic compressions where the molecules only giggle back and forth a bit, and aren't been driving in any particular direction at great speeds above their normal one.SBHarris 18:11, 11 July 2006 (UTC)
Shock waves are pressure waves that move faster than the speed of sound. Jalexbnbl 22:08, 30 August 2007 (UTC)

## Relativistic effects

When are relativistic effects important??? Should that part be removed?

Cosmologists now consider sound waves important in their description of the Big Bang. They have discovered that the equations governing sound are actually very useful to them in explaining the small variations they've observed in the 2 deg Kelvin cosmic microwave background.

They think that since the primordial universe was a liquid-like blob at extreme temperature and pressure shortly after the Big Bang, sound waves would have been able to (and did) propogate within it. The early universe supposedly also inflated faster than the speed of light. So relativistic effects would certainly be important in any detailed consideration of the baby universe. It's not trivial issue, either; those very minor differences in the pressures here and there in that early fireball created the universe we see today.

Other than that...I would think that any theoretical physicist who'd done enough serious drugs in high school that he decided to work out how fast a 'knock knock' joke would move inside a spinning neutron star (whose surface can be racing along at about 1/7th of the speed of light) would definitely need to take relativity into account. 66.11.164.72 03:48, 10 March 2006 (UTC)

(Better late than never) Relativistc affects apprear close to the speed of light in vacuum, c. This is extremly higher. All light travel (in vacuum) with the same speed - for any beholder, this isn't the case with sound. Boeing720 (talk) 00:16, 13 December 2014 (UTC)

## Picture of Fighter Jet Breaking the Sound Barrier

Shouldn't that be a rise in pressure that causes condensation? Or alternatively, a drop in pressure accompangnied by an even larger drop in temperature as a result of adiabatic cooling?

The condensation is caused by a rise in the relative humidity, which is caused by a drop in temperature, which in turn is a result of the drop in pressure. It's the same reason clouds form when air rises. Spiel496 (talk) 17:47, 23 December 2008 (UTC)

I feel that the caption to this photo is somewhat misleading. It associates the observed Prandtl–Glauert singularity with "breaking of the sound barrier" even though this effect can be observed with aircraft traveling at subsonic speeds. <http://web.archive.org/web/20070510225616/www.fluidmech.net/tutorials/sonic/prandtl-glauert-clouds.htm>

I have changed the caption slightly to explain it happens at transonic speeds (sub-thru-super). Incidentally, info identifying the image says the Hornet was breaking the sound barrier off Pusan "over the Pacific Ocean". More likely over the Korea Strait in the Sea of Japan. ):. Kaiwhakahaere (talk) 21:53, 26 September 2009 (UTC)
And just incidentally, you can tell in projectiles from the angle of the attached shock wave (which is very close to to a flat pancake 90 degrees here for the Mach angle), what the Mach number is. In the ideal weak-shock case, the Mach angle of the shock is given at arcsin(1/M) where M is the mach number. Here we have sin (~90 degrees)= ~ Mach number 1, by inspection. Higher speeds make the weak shock angle begin to bend toward being acute (Mach angles less than 90 degrees). SBHarris 06:59, 27 September 2009 (UTC)

Removing the grain kind of ruins the picture. It's going to be downsampled anyway, so it's unnecessary. But the highly filtered one we have now makes the condensation look fake and plastic, where simple downsampling gives a much more nuanced picture. Unless I hear objection I'm going to remove the filtered version and replace it with the original. (There's no reason to be doctoring this photo.) Gerweck (talk) 18:36, 31 March 2012 (UTC)

## Pressure

This is news to me. I thought sound travelled faster in high density air.

• Not as long as the ideal gas approximation holds ("mostly" empty, no quantum effects or whatnot; actually noninteracting, but that seems a little silly in this context; also, we are assuming continuum limit, with the wavelengths involved much larger than the mean free path). Metallic hydrogen (possibly) at Jupiter's core I would certainly expect to behave slightly differently from air, but in the regime we are concerned with here non-ideal effects are negligible. Basically, the interaction strength is not changing, and that governs the speed with which one molecule responds to the movement of the next.

## Sound in solids

I've added this new section, because I think it's important to note that sound also moves through media other than gases, like air. I was tempted to add the following two paragraphs to the same section, but first I would like to get some feedback. For sure they involve speed; the potential issue is whether or not they involve sound. I will leave that question to the knowledgeable jurors here:

Seismic waves generated by earthquakes are analogous to sound waves in air. Both involve compression and rarifaction of the media they are passing through. Thus the shock waves generated by an earthquake can be thought of as sound waves moving through the Earth. However, since the predominant frequency of the energy is only about 1 Hz, or lower, it's well below the audible threshold of about 20 Hz. Thus it is considered to be a pressure wave. The science of studying these waves is known as seismology.

Density of matter within the Earth increases greatly with depth, so the velocity of pressure waves is also considerably higher deep inside our planet. At extreme depths, near the Earth's core, shock or pressure or sound waves move very supersonically, at speeds as high as Mach 20 to 25, or about the velocity of the space shuttle on re-entry. Pressure waves can easily move from one quadrant of our planet to another - from China to Africa - in less than 15 minutes. Stellar-TO 22:50, 11 November 2005 (UTC)

No, no, no, no, NO! Sound velocity decreases with density. Here, let me quote Modern global seismology for you:
Since the density of the Earth increases with depth you would expect the waves to slow down with increasing depth. Why, then, do both P- and S-waves speed up as they go deeper? This can only happen because the incompressibility and rigidity of the Earth increase faster with depth than density increases.
You need to expunge this incorrect grade school knowledge from your brain. Tell everyone else too. We must to our best to kill this meme off. Maury 22:32, 14 February 2006 (UTC)

Meme is not a word I can find in my dictionary, guy! Take a memo: please expunge that non-existent word from your brain.  :)

I don't think the issue is as simple as grade school arithmetic, like you seem to believe it is. One almost has to be a physicist to understand it. I am not a physicist, but let me try to clarify.

Let's deal with the case of sound in a fluid, which much of the inner planet is, in the case of the quite large outer liquid core. See: Bulk modulus. According to that article, the adiabatic bulk modulus K is approximately given by K = aP where a is the adiabatic index and P is the pressure. In solids, Young's modulus is also measured in terms of *pressure*.

So, speed of a sound wave (or seismic shock wave, which is equivalent) in liquids or solids is proportional to the *pressure*. That is the accurate way to put it, excuse me all to heck. Increasing pressure means increasing speed. If the adiabatic bulk modulus goes up, or Young's modulus goes up, speed of the propogated energy also goes up.

However. What you have apparently ignored is that increased pressure also implies increased *density*. Which really means that density is also on the TOP part of the equation, as well as on the bottom. You cannot see it there, I know, but it is there. It's the difference between citing equations, and understanding them.

Or do you believe that putting materials under enormous pressure - like the roughly 3.5 million atmospheres at the center of the earth - will NOT squish things into a more dense state?

The average density of our planet is about 5.5 gm/cm^3. Estimated densities in gm/cm^3 are: crust: 2.2, upper mantle 3.4, lower mantle 4.4, outer core 9.9, inner core 12.8 - 13.5. The inner core is more dense than lead, which is only 11.3 gm/cm^3. It's roughly 13 times more dense than water.

That is why sound - or a shock wave - moves through it *very* fast! It's very *dense*. Don't say NO NO NO...because your brain has looked at only HALF the equation, the bottom part. (Where density appears, formally.) You have to look at the TOP part, too. What does ENORMOUS PRESSURE imply? It implies a change in density, to greater. Yeah? Yeah. So...increasing pressure means increasing density...means speed goes *UP*.

Pressure dictates the speed, but it also dictates density! They are *both* linked to it. If pressure goes up...they both go up. Right?

So...effectively...in the equation for the speed of sound, in solids or liquids: density is in the TOP part of the equation, too. Because *pressure* is there! That's why it's not entirely accurate to allege that speed *decreases* with density, if you're talking about the inner planet. Which is what I was talking about. You cannot vary the pressure without varying density, as well.

So I say again: speed goes *UP* with density!!! Not *DOWN*, you sonic infidel. But I admit: the governing reason is the *PRESSURE*. There. I am so profoundly grateful to you for inspiring me to clarify my somewhat clumsily inadquate point. Excuse me, and thank you!  :) 66.11.164.72 01:55, 10 March 2006 (UTC)

## Experiments to measure the speed of sound

Should we add a section on the classic methods for the measurement of the speed of sound (for instance Kundt's tube) ? Cadmium 14:14, 1 January 2006 (UTC)

In an overview style which doesn't get too practical, what could be a reason not to? Femto 15:18, 1 January 2006 (UTC)

## Universal gas constant

If you divide the universal gas constant by the molar mass of a specific gas, you cannot possibly end up with the universal gas constant again. Many people call that a "specific gas constant", some may have other names, but "universal gas constant" is positively wrong. Unfortunately, the current gas constant article adds to the confusion, I'll take the issue there as well. Algae 20:14, 1 January 2006 (UTC)

May I support this point: at least for physicists, there is only one universal gas constant R: the Boltzmann constant times the Avogadro number. The use of an air-specific constant R in this article is highly confusing and should be avoided. Please replace R by R/M and adjust the explanation. The resulting formula would apply to arbitrary (degrees of freedom, molar mass) ideal gases. Nils Blümer 20:13, 3 February 2006 (UTC)

## Problem with the pressure statement (and speed is 331.6, not 331.5)

The first paragraph of this sound article states clearly that static pressure has no effect upon the speed of sound. This is patently false, which I can vouch for as a physicist myself. Go get any elementary college physics text and you'll see that this is false. For example, I'll dig one up for you: look at Physics, 2nd ed., by Ohanian. Chapter 17, equation (3) clearly states that, "...the theoretical formula for the speed of sound is Vs = root(1.4*Po/po), where Po and po designate the UNPERTURBED [i.e. static] PRESSURE AND DENSITY, respectively." On top of this fact, this article itself then gives equations at the bottom of the page in terms of air pressure. Another problem, the incorrect sentence writes Static Pressure (Air Pressure) as if the two were the same thing, but if you read both articles you see that they are not. I'm deleting the error in the first paragraph; if you revert my corrections, please for the sake of all that is proper physics provide your sources. Thanks Astrobayes 21:27, 18 March 2006 (UTC)

• ...and looking closely now at the initial equation given for the speed of sound in air... it's not at all consistent with the mathematics of the temperature-speed relation of sound in air. For one, where did the author get 331.5 m/s? The common equation in most physics texts lists only 331 m/s. Is this a big difference? To a physicist, probably. To a mathematician, yes. Also, where is the 0.6 coming from? The relation inside the root should be as follows: root(1+ Temp/273), with Temp in Kelvins. This can be verified in most every college physics text if you have a little algebra background. So I ask you this, author: Where is your source for this equation? (title, author(s), and page numbers please). We are doing a disservice to the general public by putting up information that is wrong or appears wrong without citation. Thanks. Astrobayes 21:59, 18 March 2006 (UTC)
Well, if you put everything in to 4 sig digits, it actually comes out 331.6, as I make it. The temp is 273.15, R is 8.3145, air gamma is measured at 1.403, and finally the mean molecular weight of DRY air is 0.02897 kg/mole. Dividing this R by this MW gives the air specific value of R/M of 287.003 whereas 287.05 is used in the article. Close enough. I actually can't get down to 331.5 (rather than 331.6) even with temp at 273.00 exactly (that comes out 331.55).Steve 21:17, 5 July 2006 (UTC)
And where is the 0.6 coming from? It's the coefficient of the first term in the Taylor expansion of the equation you give, of course. Higher orders are being neglected.Steve 21:58, 5 July 2006 (UTC)
Here's a cite: [1]
Hi. I just wanted to point out a probable mistake in the section "Dependence on the properties of the medium", par. 4. The first sentence reads "(...)pressure and density are inversely related at a given temperature and composition(...)" which I think is false[1]. Firstly, for constant mass ρ≈1/V. Then, from the clapeyron, P≈1/V with constant temp. and amount of gas. From that it is evident that 1/V≈1/V, or P≈ρ.(ρ-density, P-pressure, V-volume) Please correct me if i'm wrong or misinterpreting the information. Also feel free to move this note wherever it would be suitable, as I'm a first time poster. thanks 178.42.38.49 (talk) 00:03, 5 June 2015 (UTC)

## Basic concept

The intro paragraph stresses how important temperature is on the speed of sound, but is never brought up in the analogy used in the Basic concept paragraph. Using the ball/spring model it is easy to visualise why density plays a role, but why is temperature excluded? Is this because the analogy fails to explain it? Does the speed of sound vary with increased temperature because of the increased average vibration energy in a medium? How? I think the temperature effect needs to be addressed before beginning the math. --Daleh 14:41, 27 August 2006 (UTC)

I've been going 'round and 'round about this in the, Electrotech Forums (where I'm considered pretty much an ignorant pest). The "balls separated by springs" analogy (and its counterparts) seems to be very firmly ingrained in the minds of the physics world.

But, you're right, it doesn't even address the temperature issue (much less answer it). We are asked to believe, for example, that the repulsive force of neighboring molecules substantially changes with temperature and very little with how close they may be packed together. That the thin air at 30,000 feet and the denser air at sea level can have the same Mach number so long as their temperature is the same based...on the "stiffness" of the mutual repulsive force of the air molecules.

Eventually, I came up with a scenario that I believe at least addresses the temperature issue and reference it here for analysis:

http://www.electro-tech-online.com/math-physics/87198-why-does-sound-propagate-14.html

Start near the bottom of that pge wiht the post by, Crashsite titled, "Got It". Also see the next few following posts.

I have to say that there's still a piece missing. And, it's the same one that's missing from the "ball and spring" model. Exactly how a subsonic disturbance is suddenly and near instantly accelerated to Mach 1 and then propagated at that speed. Like, Daleh seems to, I suspect that it has something to do with the natural vibrational speed of the molecules due to temperature but, I haven't quite figured out just how and my math skills are too poor to deduce it that way. Crashsite55 (talk) 03:03, 28 May 2009 (UTC)

I didn't find the "got it" post very illuminating. It's difficult for me to get my head around a microscopic description of sound. (One interesting aside, the speed of sound in a gas is always comparable to the root-mean-square velocity of the molecules. )
In my opinion, the confusion begins when we try to equate the gas molecules to the balls in the ball-and-spring model. It's a tempting path to take, but the analogy breaks down immediately; there is no spring force between the gas molecules. The ball-and-spring model can still be applied, but the "ball" should be a parcel of air -- a volume much larger than the distance between molecules, but smaller than the wavelength of the sound. The spring constant corresponds to compressibility of the air. Then if we relate the mass and the compressibility to temperature and pressure, we're done. Spiel496 (talk) 15:46, 28 May 2009 (UTC)

There is an inserted picture relating to the "sound barrier" of which there is no mention except at the bottom (see also). Is this picture for the 'thrill' factor ? Preroll (talk) 02:47, 14 October 2010 (UTC)

## 331.6 m/s

Should we use the speed of sound for 0 °C as 331.5 or 331.6 m/s?
The answer seems very clear. --Tom 5:27, 28 September 2006 (UTC)

Yeah, but that doesn't mean it's right. Using the best numbers available, and the equation given in the article, it's clearly 331.6, not 331.5 m/sec.

Don't trust Google as a source of info, for quite often it ends up reflecting errors in Wikipedia these days. Not too long ago I caught Wikipedia in an error on the number of spikes in the seed capsule in the American Sweetgum, a tree that lines the street where I live. Wikipedia said there were 40 to 60 capsules per gumball, each with 1 spike. In fact, there are twice that many spikes betcause there are TWO per capsule, as anybody can verify by simply counting them (there are about 100). But the wrong information (which included several recent texts) had spread from Wikipedia all across the net. We changed it, and now the correct numbers are spreading in the reverse way. It's Stephen King's Word Processor of the Gods-- change the entry to change reality. Unless you want to go out to your yard and actually look for yourself, that is. SBHarris 19:32, 3 October 2006 (UTC)

In any case, it's not 331.4 or 331.3, which give a roll-off number of google hits, if you type in "speed of sound 331.x" with different x values. Doing this, the clear Google most popular value for speed of sound in dry air at 0 C, is 331.5 m/sec. And I can find various official sources for nearly all of these numbers, so that's no help. As noted above, if you use the available numbers to 5 sig digits for dry air at 0 C, the theoretical is 331.6. But I'm happy to leave it at 331.5, which is at least close. I note that a recent editor has changed this all to 331.3, and as that's clearly way off the theoretical and popular answer, I'm reverting it back to 331.5. If anybody has a really good argument (a recent US Bureau of Standards measurement or something that is 4-digit accurate), please post here. SBHarris 21:04, 30 December 2006 (UTC)
A credible value of R is 8314.472. Credible values for gamma range from 1.3991 to 1.402. A credible value for the molar mass of air is approximately 28.965. Let's calculate in 5 digits: c=sqrt(gamma*(8314.5/28.965)*273.15) This gives a value that ranges from 331.21 to 331.55. Using the value commonly given for gamma (1.400 - not 5 digits, BTW) we get 331.32.--Ron E 18:25, 25 February 2007 (UTC)
Digging for a more accurate gamma relation, I found one at http://users.wpi.edu/~ierardi/PDF/air_cp_plot.pdf Given c_(273.15K)=sqrt(gamma*(R/M)*273.15) and that gamma =Cp/Cv, from which data we can calculate gamma to be 1.4000 using R=8314.472 and M=28.9645 and the relation Cv=(Cp-R/M). This gives 331.32 as the coefficient in your sound speed equation.--Ron E 19:28, 25 February 2007 (UTC) -edit--corrected Cv eq'n--Ron E 22:22, 26 February 2007 (UTC)
Thanks for changing all those 331.5's I missed. Yeah, basically we agree that 331.3 m/sec at 0 C in dry air is what you get for the best numbers for gamma = 7/5 exactly, and the most commonly found search value of 331.5 cannot be gotten except by assuming gamma is about 1.403, which is at the upper end of experimentally measured values for it. But I've bowed to kinetic theory here, and used the 1.4000 gamma value. And left a note for those puzzling over where other values than 331.3 might come from. Some of them actually were probably measured directly. SBHarris 23:00, 26 February 2007 (UTC)
The "Effect of temperature" table is now inconsistent with the formula. Look at the values. They increase 3.0 m/s for each 5°C increment, except for a newly-created glitch at 0°C. Spiel496 23:51, 26 February 2007 (UTC)
This should be fixed now. To [User:Sbharris] above: I think that the value 331.3 is more correct for several reasons. First, since the equation makes the assumption of ideal gas, we should use "ideal gas" values in the entire derivation. Second, quoted values of gamma actually do range over at least the values quoted in the article and the curve fit I cite above does give a value of ~1.39996 at 0C and 1.3996 at 25C if I did my math correctly.--Ron E 00:34, 27 February 2007 (UTC)

I did some work in the early 90's on the speed of sound in air that was published in J. Acoust. Soc. Am., 93, p2510, 1993. I was working realizing a National Standard for sound pressure level by reciprocity calibration of reference condenser microphiones in South Africa. Beacuse our lab was at high altitude near Johannesburg(about 85kpa) we needed to take pressure into account. I started off using some work that had been done by George Wong of the NRC in Canada, who was doing the same type of work on microphones. However when trying to use Wong's values in my own calculation including pressure coefficients, I found some discrepancies. The above-referenced paper addresses the details. I note that it appears that the approximate formula that I generated was proposed for use in European Metrology Laboratories [K Rasmussen, 1997 Calculation methods for the physical properties of air used in the calibration of microphones]. Rasmussen was the chair of the IEC committee that was standardizing microphone calibration procedures. My value of the speed of sound in dry CO2 free air at 0 deg C was 331.45 m/s, and this was calculated using virial coefficients to account for departures of the gaseous constituents of standard air from Ideal gasses. I beleive that this accounted for the discrepancy between my work and the work of Wong, who had used some ideal gas values. I beleive that my work and other work supports a value of 331.45 or rounded up to 331.5, if this level of precision is required. [Owen Cramer, 20 Sept 2007]

The International Critical Tables (1929) also give V0 = 331.45. Curiously, they note that the value for V0 progressively decreased by 0.3 percent from 1738 to 1919, "suggesting a slight change in the constitution of the atmosphere".
They also give a formula for the speed at temperature t (degrees C) as V = 330.6*sqrt(1 + 0.003707*t - 1.256E-7*t*t). DonPMitchell (talk) 06:29, 25 June 2008 (UTC)

## Speed of sound in solid

Probable mistake: The stated Young´s modulus for Yttrium Iron Garnet, 2000 GPa, seems way off. In the wiki article on Young´s modulus it is stated as 193 GPa. The lower value appears in several places on the web, but I have only found the higher value in one place, where it is listed as 2*10^12. That is the webpage listed as reference #16, BTW. If that higher value were true, YIG would be four times as stiff as tungsten, and almost double the stiffness of diamond. —Preceding unsigned comment added by 83.209.73.77 (talk) 10:40, 15 January 2009 (UTC)

In a solid rod (with thickness much smaller than the wavelength) the speed of sound is given by:

${\displaystyle c_{\mathrm {solids} }={\sqrt {\frac {E}{\rho }}}}$

where

E is Young's modulus
${\displaystyle \rho }$ (rho) is density

Thus in steel the speed of sound is approximately 5100 m·s-1.

Would someone like to educate the human race as to what units this equation uses to derive this conclusion? Because try as I might, I can't figure it out. You divide GPa by kg/m3, take the square root, and somehow arrive at m/s ? Neat trick. —The preceding unsigned comment was added by 76.209.59.227 (talk) 04:32, 21 January 2007 (UTC).

${\displaystyle {\sqrt {\frac {Pa}{kg/m^{3}}}}={\sqrt {\frac {N/m^{2}}{kg/m^{3}}}}={\sqrt {\frac {(kg*m/sec^{2})/m^{2}}{kg/m^{3}}}}={\sqrt {\frac {m^{2}}{sec^{2}}}}={\frac {m}{s}}}$
Spiel496 16:01, 21 January 2007 (UTC)
• Very nice, Spiel496. I might add a bit of mental mnemonic helps sometimes: whenever you see pressure in an equation, just remember PV = work = E, so pressure always ALSO has units of energy/volume = E/V. If you divide a pressure by density, the volume cancels and you get energy per mass. Now, remember your Newtonian kinetics or your relativity: anytime you take the square root of E/m you're going to get a velocity. SBHarris 16:31, 21 January 2007 (UTC)
• Why is it marked m·s-1? Shouldn't it be 5100 m/s? What would a speed of 5100 m·s-1 actually mean? My math isn't good enough to consider taking the responsibility to change it, but my BS meter is going off. -- S. Gartner talk 21:52, 13 April 2007 (UTC)
s-1 and 1/s are exactly the same thing. That's just algebra; I don't think anyone was trying to be confusing. But if this m·s-1 nomenclature is confusing to the typical reader, I don't have a problem if they all change to m/s. Spiel496 06:28, 14 April 2007 (UTC)

## Speed in a liquid

I have never edited a page before, and am more happy to bring this up in the discussion. The article says that the Chen-Millero-Li Equation (1994) is more accurate than V. A. Del Grosso (1974). But in my research I came across a paper in the The Journal of the Acoustical Society of America that empiricaly showed Del Grosso is more accurate than Chen-Millero-Li. Article Abstract. Also stubled into this paper that show Del Grosso as being more accurate than Chen-Millero dushaw-jasa-93 71.39.95.25 21:26, 23 January 2007 (UTC)

Two cites are quite good enough to change the statement in the paper, and you could have done yourself (jump in!). Would be interesting to find out why the later equation was presented when it's not as good. It must have had originating data to go with it which claimed the opposite. So perhaps there's a conflict. However, most references win at this point. SBHarris 21:32, 23 January 2007 (UTC)
I've taken a look at the paper behind the cited abstract, and it seems to me that the precise accuracy of Del Grosso v. the revised Chen-Millero-Li equations should perhaps be considered still a research question - the error bars are large (the original Chen-Millero equation is a non-starter). All the differences are slight, however, being at most a couple/few tenth's of a m/s in sound speed of 1500 m/s. I mainly wanted to point out that Del Grosso's equation is only for sea water - you'll get into "real trouble" with it in e.g., brackish water. The Chen-Millero-Li equation, while it may have issues, is at least generally applicable in a wider range of water - I believe that paper states as much. As Dushaw et al point out, these equations are found by fitting polynomials to data, so for values of T, S, P where there was no data the sound speeds get really wrong in a hurry. Del Grosso's measurements spanned just the range of normal sea water. The article section is "speed of sound in liquid" - so it is important to be clear about where the equations can be used - there is no universal sound speed equation in fluids (water) that I know of, the closest being Chen-Millero-Li. I believe there are also equations specifically for fresh water. (In the early '70's sound speed equations were all the rage.) I plead conflict of interest and recuse myself from editing, however (having already edited enough here!) Perhaps a sub-subsection on the speed of sound in seawater? Perhaps change the section title to speed of sound in water? Bdushaw 16:24, 29 July 2007 (UTC)
I don't know what the official wikipedia policy on this is, but personally I trust the opinion of an expert, and as such, Bdushaw is better qualified than most to edit the relevant section. Apart from the inappropriate title, is your point that regions of validity of the various equations are not clearly stated? (That could be solved by referring to a review article like Fisher & Worcester in [Crocker 1997]). For my own ha'pennies worth:
1) I agree it's about the speed of sound in seawater and should be retitled to reflect that;
2) I reworded the text a couple of months ago as it seemed to overstate the case for Del Grosso (cf Chen-Millero), but the existing wording seems neutral to me. Does anyone disagree?
3) It should be pointed out somewhere that Chen-Millero is the UNESCO standard, as far as I know *without* the correction proposed by Li [N. P. Fofonoff & R. C. Millard Jr, Algorithms for computation of fundamental properties of seawater, Unesco technical papers in marine science 44 (UNESCO, 1983).]. Has it been updated since then?
4) There's an excellent monologue on this subject written by CC Leroy [C. C. Leroy, The speed of sound in pure and neptunian water, in Handbook of Elastic Properties of Solids, Liquids and Gases, ed Levy, Bass & Stern, Volume IV: Elastic Properties of Fluids: Liquids and Gases (Academic Press, 2001) ]
Thunderbird2 17:15, 29 July 2007 (UTC)

Altitude of commercial jets. - Most jets fly much lower than 11000m. If you're on a short hop, you might be at 29,000 ft-31,000. For transatlantic flights, 35,000ft < 11000m.

## effect of frequency

According to p351 of Wood 1946 (who quotes from early work by Herzfeld and Rice) "... the adiabatic state is best guaranteed for the low frequencies, while for the higher frequencies the influence of heat conduction is larger ...". Unless this statement is challenged by more recent research I suggest the paragraph about frequency dependence be either deleted or reversed.

REF: A B Wood, A Textbook of Sound (Bell, London, 1946)

Thunderbird2 21:50, 8 July 2007 (UTC)

## Standard atmosphere at sea level

The speed of sound varies with the medium employed, as well as with the properties of the medium, especially temperature. The term is commonly used to refer specifically to the speed of sound in air. At sea level, at a temperature of 21 °C (70 °F) and under normal atmospheric conditions, the speed of sound is 344 m/s.

It makes no sense to give the speed of sound adding the words at the "standard atmosphere at sea level". We have the formula:

${\displaystyle c={\sqrt {\gamma \cdot {p \over \rho }}}\,}$

Statement: The air pressure p and the density ρ of air are proportional at the same temperature. That means, the fraction p / ρ is always constant, even at "sea level". Cross always the useless words "At sea level". If the temperature is the same, we get the the same speed of sound down at sea level and high on a mountain.

John 21:50, 5 September 2007 (UTC)

## Speed of sound

Can the speed of sound rise in above its original speed in air (or any substances for that matter)LearnguyLearnguy (talk) 17:09, 27 April 2008 (UTC)?

After an explosion which expands faster than the speed of sound, there is a continuing disturbance called a hypershock which moves outward, faster than sound. Whether you consider it sound or not, is semantics. It's a bulk movement of a mass of air, which moves in a wave. It quickly slows to sonic velocity, and then propagates at that rate with less loss of energy over distance. SBHarris 08:29, 29 October 2008 (UTC)

## Math error in the first paragraph

The opening paragraph says "...343 m/s. This also equates to 1235 km/h, 767 mph, 1129 ft/s" By my calculation, 343 m/s = 1125.328048 ft/s which is easily enough rounded down to 1125 ft/s. The mistake is probably the result of someone changing the reference to 343 m/s from a previous notation of 344 m/s. I will correct the f/s calculation. MRJayMach (talk) 14:08, 16 September 2008 (UTC)

I suggest that the numbers in the first paragraph be reviewed. I corrected someone's vandalism but the numbers still don't look right. Rosattin (talk) 07:57, 26 December 2008 (UTC)

The link to an article in New Scientist magazine (http://space.newscientist.com/article/mg19826504.200-did-sound-once-travel-at-light-speed.html?feedId=online-news_rss20) is frustrating as it leads to just the first few paragraphs of an article and then requires the reader to buy a subscription to read on. Such links serve commerce rather than the reader, and it seems to me that they are best avoided - or at least flagged as a tease. But before or rather than immediately deleting it I thought I should ask if other readers feel the same way... Sng

## “Basic Concept” U/Fe example

The “Basic Concept” section gives the following example:

All other things being equal, sound will travel more slowly in denser materials, and faster in stiffer ones. For instance, sound will travel faster in iron than uranium, and faster in hydrogen than nitrogen, due to the lower density of the first material of each set.

I'm pretty sure uranium is stiffer than iron, so the “all else equal” premise is not satisfied. The solids example might be replaced, for instance, with iron and carbon steel: the density should be similar, but the stiffness can vary widely.

• A good point, and we need to find two metals which are better matched, either for one property or the other. As you can see, somebody was trying for a match with stiffness with metals of very different density. I don't know what the stiffnesses are for very pure iron and uranium, though I know that very pure iron is quite soft-- reputably bendable by hand. In any case, agree that another example is needed.SBHarris 01:23, 12 January 2010 (UTC)

It might also be a good idea to replace one of the gases such that they have the molecular structure. In this case, both hydrogen and nitrogen are diatomic, but the N–N link is rigid for torsion while the H–H link allows rotation. The article earlier mentions indirectly that the freedoms of the molecules is a factor, so this also violates the “all else equal” premise. I'm not sure that's very significant, but it's no big deal to replace nitrogen with any halogen (F, Cl), thus making sure that only the density changes.

• Here, on the other hand, the example is physically okay because the rotational degree of freedom around H2's sigma bond doesn't give it any extra heat capacity. The reason is the moment of inertia around this bond is set only by the rotational moment of inertia of a single atom, which is very small because the nucleus is compact and the electrons are very light. So none of the "rotation about the bond axis" modes are exited at all, and it might as well be oxygen or nitrogen; it will have the same heat capacity. But yes, just so somebody doesn't get the wrong idea, I agree that "nitrogen" here could be replaced by fluorine. Or we could use hydrogen and deuterium, where density is even more of a "only difference", but the sound speeds differ by a factor of (square root 2) = 1.414. SBHarris 01:22, 12 January 2010 (UTC)

## Incorrect values in table?

I created a table in OpenOffice Calc with temperatures per degree from -30˚C +35˚C, using the formula 331.3 + 0.606 * C, and the numbers vary with the ones listed in the table at Speed_of_sound#Tables. They match at 0˚C and 5˚C, but already at -5˚C and at +10˚C, they vary. My numbers are available here. Should the wikipedia table be updated, or are my numbers wrong? Rkarlsba (talk) 11:42, 3 September 2010 (UTC)

The formula is an approximation. The table values are (I think) more accurate. Spiel496 (talk) 13:51, 3 September 2010 (UTC)

## China Airlines 006

I'm pretty sure that somewhere there's a bit about China Airlines Flight 006 "almost certainly" breaking the sound barrier, but I can't seem to find it. Can anyone help me out here? —Preceding unsigned comment added by 66.189.116.112 (talk) 23:42, 28 September 2010 (UTC)

Oh, and I forgot earlier, I think there was a part in the same section about a DC-8 also possibly breaking the sound barrier in a shallow dive during a test flight. Can't remember the date.66.189.116.112 (talk) 23:48, 28 September 2010 (UTC)

## Ambiguous introduction

The introduction states that the speed of sound in iron is 5,120 m/s, and then in the next paragraph states that the speed of sound in solids depends on whether the wave is transverse or longitudinal. So when the "speed of sound" is stated for a solid material such as iron, as it was above, is there a convention as to which speed is the one being referred to? I would assume it's the longitudinal case, because the paragraph is comparing it with the speed in various fluids, which carry longitudinal waves only. --JB Gnome (talk) 22:54, 7 December 2010 (UTC)

That's a very good question. In this case we know it's the longitudinal wave, because shear waves in iron only travel about 3000 m/sec. However, you never know what kind of wave speed you have until you know the system. Sometimes these things are given as speeds in "long thin rods," which you would THINK would have the same longitudinal-compression velocity as an infinite 3-D solid, except it doesn't. I can't think of an intuitive reason why not, but the speeds are not the same. Also, long thin rods have additional modes of shear stress waves that one doesn't find at all in a 3-D solid. These include torsion waves, and a kind of bending wave like a wave of vibration on a metal wire, neither of which even happen in 3-D solids. SBHarris 02:10, 8 December 2010 (UTC)
In thin rods, the rod expands and contracts radially as the sound wave passes (assuming Poisson's ratio is nonzero). In an infinite solid, it is constrained from doing so. Thus the speed difference. Anyway, yes, "speed of sound" without qualifiers usually means speed of pressure waves, rather than speed of shear waves, although that's not a real convention, nor should it be. Norman Yarvin (talk) 17:32, 8 December 2010 (UTC)
Ah, thanks Norman. The things you learn while writing. Looking into this, I see that for thin rods the Young's modulus Y simply replaces the bulk modulus B in the equation, and that Y = 3B(1-2v) where v is Poisson's ratio. Figuring this at 0.3 (reasonable for metals like steel) that gives you Y = 3B(1-.6) = 1.2 B. Which means that sound travels FASTER in the thin rod by a factor of SQRT(1.2) =1.095. The ratio of rod/bulk speeds depends on Poisson's ratio: if it's larger than 0.33, a quite reasonable value, then it's easy to see that sound travels slower in thin rods than bulk, if it's less than 0.33, it goes faster in thin rods than bulk. Real values can be on either side of this value with non-zero and non-negative Poisson ratios (which must be from -1 to +1/2). So, again it's not that intuitive. If energy went into thin rod radial expansions and contractions I would presume that mostly sound would travel slower in thin rods, due to having this extra "way" to store compression-energy. SBHarris 23:12, 8 December 2010 (UTC)

## Thin rods

${\displaystyle {\frac {c_{\mathrm {rod} }}{c_{\mathrm {bulk} }}}={\frac {\sqrt {\frac {Y}{\rho }}}{\sqrt {\frac {Y(1-\nu )}{\rho (1+\nu )(1-2\nu )}}}}={\sqrt {\frac {(1+\nu )(1-2\nu )}{(1-\nu )}}}}$

The two speeds are equal only when Poisson's ratio is equal to zero. This is possible, as Poisson's ratio can take on values from -1 to +1/2 for materials. In a metal, where Poisson's ratio might typically be +1/3, the ratio of the speeds would be 2/3, meaning that the speed of sound is 50% faster in the bulk material than in the long, thin rod. I think this is right, but need to check before putting it in. Are there separate compression and sheer waves in a thin rod, or just one type of tangent-sheer wave? SBHarris 19:32, 28 July 2011 (UTC)

## Plot in "Practical Formula" section

Does the plot in the Practical Formula section add value to the article? The green trace is an "Approximation of the speed of sound in dry air based on the heat capacity ratio" and the red trace is the Taylor series approximation. While it would be interesting to compare an approximation to the actual speed of sound, I don't feel it benefits the article to compare two approximations. All we're doing is showing that sqrt(1+x) ≈ 1+x/2, which not specific to the phenomenon of sound. Furthermore, the plot may mislead the reader that the green trace is accurate, even near absolute zero, where it's probably not. Spiel496 (talk) 21:42, 19 September 2011 (UTC)

No one came to its defense, so I removed it. Spiel496 (talk) 19:05, 17 November 2011 (UTC)
Sorry, but I didn't notice your note. I've reverted removal of the graph, only for WP:BRD reasons-- I don't mean to be snarky. My defense argument is that it's not obvious from looking at THIS Taylor expansion that it gives the same results as the square root form, for -100 to +100 C, but diverges badly at colder and higher temps. Sure that's all in the equation, but you can't look at just the equation and realize that without the graph, unless you're a quantitative genius. The goodness of the Taylor expansion itself depends on the value of "x," the temp, with regard to the coefficients, so we're comparing y= A sqrt (1 + bx) to y = A (1 + bx/2), and x can be positive or negative, so it's not all that obvious what values of -x to +x are going to give y to within some fraction of a percent, in the expansion. Can YOU see the -100 to +100 C "good" range? I certainly agree that a plot of real values would help, but just knowing the valid range of the Taylor expansion with regard to the best analytic form (the square root equation) is helpful. SBHarris 19:27, 17 November 2011 (UTC)
Good point, and no "snark" taken. Still, I think it would be an improvement to limit the temperatures to a range where we know the square root function is valid. Can we at least keep it above 100 Kelvin? Liquid nitrogen doesn't behave as an ideal gas. Spiel496 (talk) 19:52, 17 November 2011 (UTC)
Helium still does, though. I'll see if I can stick in some kind of qualification. The problem is that all these things depends on the reduced properties of gases (reduced pressures, reduced temperatures, etc), where these things are expressed in terms of the critical temps and pressures for the particular gas in question. For the validity of the square-root equation at the hot end, it depends on gamma staying constant, which in turn depends on on it being monatomic. For diatomics, to use gamma=7/5 it must be cold enough for the OTHER type of reduced temperature (T/theta, where theta is the Einstein temp) to be small. Otherwise gamma creaps up toward 9/7... SBHarris 20:24, 17 November 2011 (UTC)

## Unwarranted accuracy in altitude dependence table?

How can the speed of sound be 1062 kph over the entire range of 11,000 to 20,000 m? I was hoping to be able to determine the speed of sound at the altitude where the sound barrier was first broken by a wheeled vehicle, namely 4000 feet, by interpolation from such a table (since lapse rate is essentially linear with altitude), but this table doesn't seem to serve that purpose. --Vaughan Pratt (talk) 18:26, 15 July 2012 (UTC)

I can well believe that sound speed is nearly unchanged through that range, since temp is stable with altitude through that area. See the following illustration from the WP article "Atmosphere of Earth":
See the three straight up-and-down temp sections, in red? The speed of sound is constant through these altitudes, also. There's a graph for THAT, in blue (I should add this graph to this article, if it's not already here). See THIS article about why sound speed varies only with temp, not pressure or density per se, in the atmosphere. SBHarris 20:42, 15 July 2012 (UTC)

## speed in various stuff

How about a table of speed of sound in various mediums? Some of them are mentioned in the article, though. 85.217.39.114 (talk) 14:06, 30 July 2012 (UTC)

The problem with such a table is that there are millions of kinds of "stuff." How do you limit it? You'd have to be very careful about having a few types of metals, a few types of crystals, a few types of liquids, and a few types of gases, all chosen carefully to illustrate the very ends of the ranges (gasses, for example, from hydrogen to UF6; metals from beryllium to lead)SBHarris 18:28, 30 July 2012 (UTC)
How about a list with every matter of any kind? :D 85.217.46.150 (talk) 01:17, 10 August 2012 (UTC)
Sounds like a great idea for a list article per WP:LIST. Get to work! In the old days (when people were manic-crazy here) there was actually an article called List of Chinese people. Now, that's ambition. But there's still a List of Hong Kong people and a List of Chinese Americans, see [2] So I'm not making this up! SBHarris 05:33, 10 August 2012 (UTC)

## Intro sentence

Shouldn't the intro sentence stating the speed of sound in dry air at a given temperature also specify the altitude (or, more specifically, air pressure) ? The speed of sound in a gaseous medium does change with pressure, right? I'm no physicist so I thought I'd post this here rather than make the edit myself. I'm assuming the speed given is at sea-level, but I'm not sure.

Thanks!

Spiral5800 (talk) 00:59, 27 September 2012 (UTC)

Sigh. Read farther and learn, dude! The speed of sound in an ideal gas is actually dependent on temperature only, and is NOT dependent on pressure. This is noted right in the lead of this article, and in explained in detail farther down. Don't you suppose it might be a good idea for you to read PAST the first sentence, before suggesting a change? SBHarris 01:15, 27 September 2012 (UTC)

## mach number

The section on Mach number is very confusing.

It gives a complicated formula for "computing Mach number." The formula for computing Mach number is actually very simple: Take your speed. Divide it by the speed of sound. That's the Mach number.

I suggest deleting everything in this section following the words "Mach number is a function of temperature," since it's not very relevant to the subject. People who want to know how to compute Mach number in the case that you know neither your speed nor the speed of sound should go to the article on Mach number.

Geoffrey.landis (talk) 16:00, 3 October 2012 (UTC)

This section does have some problems but it is giving more information than just "speed divided by speed of sound". It tells you your speed based on the measured pressure in a Pitot tube. Spiel496 (talk) 05:40, 4 October 2012 (UTC)
It does. Why is that information here? In the absence of an article "How to Measure Speed in Transsonic flight Using a Pitot Tube," I cut this material out of this article and pasted it into Mach number.
for this article, it's relevant that Mach number equals speed divided by the speed of sound, but is all that's needed. Geoffrey.landis (talk) 21:22, 15 October 2012 (UTC)
Okay, but Mach number already had a version of these equations. I appreciate that you're being careful not to destroy information, but that was a bit clumsy. Spiel496 (talk) 22:57, 15 October 2012 (UTC)

## error and misleading precision in value given for speed of sound in air

The article currently gives the speed of sound in dry air, at standard temperature, as 343.2 m/s. This is both wrong and misleading in the precision claimed. This value appears to have been cooked up as follows. Take the adiabatic index to be 1.400, T=293.15 K, and the molecular weight of air to be 28.9644 g/mol (the value from the US Standard Atmosphere). Plugging in numbers gives 343.24 m/s. This is wrong because air contains traces of gases that are not diatomic, so the adiabatic index isn't exactly 1.4. The article itself cites measured values ranging from 1.3991 to 1.403, with the middle of the range being a little higher than the diatomic value, presumably because of the presence of monoatomic gases such as argon, and despite the presence of polyatomic gases such as methane. Taking the middle of the range for the adiabatic index gives 343.36 m/s, the low end of the range gives 343.11 m/s, and the high end of the range gives 343.60 m/s. It clearly doesn't make sense to take a molecular weight from the USSA, but use an adiabatic index that isn't consistent with the mixture of gases defined in the USSA. What this really demonstrates is simply that it's silly to try to give the speed of sound in dry air at standard temperature to a precision of a tenth of a meter per second. The experimental range of variation of the adiabatic index is enough to make this precision meaningless. This is presumably why one sees a variety of values floating around on the internet. My students seem to be finding 343.2 m/s (presumably from WP) and also 343.6 m/s. My students' naivete about significant figures isn't by itself a reason to delete this sig fig from the article, but the considerations above show that the digit is not in fact significant given the experimental state of the art, and in any case has been derived from an inconsistent set of assumptions. (Much bigger changes would also result from temperature changes of a fraction of a degree, or a tiny bit of humidity.) For these reasons, I'm going to delete the final sig fig from the article.--207.233.84.11 (talk) 19:26, 20 February 2014 (UTC)

Some presumably well-meaning person reinserted the bogus significant figure, and even added another bogus one, giving the speed of sound to 5 sig figs. This is wrong, for the reasons given above. I've re-deleted the false precision.--207.233.86.179 (talk) 23:48, 14 February 2017 (UTC)

## c for celerity

Any value in adding a comment to the equations section that the letter "c" in the equations is based on the word "celerity"? (As opposed to using "v" for velocity). 99.245.230.105 (talk) 09:37, 8 March 2014 (UTC)

my response (sorry don't know how to annotate properly): This article is about speed, which is a scalar quantity, "velocity" is a vector, so there would be no need to use "v" or "velocity".

That page makes it clear that "c" was used because it's the first letter of "celeritas", but it also refers directly to the speed of light.

BTW, if someone does see fit to add a section about "celerity", please don't use "celerity" - use the correct Latin "celeritas".

However it also raises questions about the use of "c" for the speed of sound. "c" is most often used for speed of light, e.g. E=mc2, and I always thought it was reserved for that purpose, but apparently it is also used for the speed of sound (news to me). Perhaps discussion of the applicability of the symbol "c" is outside the scope of this article? Perhaps a separate article talking about the original of some of the symbols in use in Physics & Mathematics? — Preceding unsigned comment added by 69.196.132.83 (talk) 16:57, 21 June 2015 (UTC)

## remove commas and periods from equation images

Someone should remake the equation images to remove the trailing "," (comma) and "." (period). I see they are also in the alt text expression. Those punctuation marks don't belong in the equations. It looks particularly bad for 273.15 - one occurrence has a "." above it and the other has it after the 5, i.e. "273.15." If you want to add punctuation to the article, e.g. commas between several items (equations?), then do it in the HTML markup, not in the equation images. In fact, I would not even put those commas and periods in the article, i.e. when listing several equations or including an equation in the narrative.

For example: https://upload.wikimedia.org/math/9/3/f/93fe3a13923fef7a15be23e5c7fb6fed.png — Preceding unsigned comment added by 69.196.151.159 (talk) 17:26, 21 June 2015 (UTC)

Equations in a sentence should be punctuated. LaTeX equtions should have punctuation within the [itex] tags (which puts them in the equation image) or else weird formatting thing can happen. See MOS:MATH#PUNC. Mysticdan (talk) 21:42, 12 August 2015 (UTC)

## Heat capacity ratio

"In gases, adiabatic compressibility is directly related to pressure through the heat capacity ratio (adiabatic index), and pressure and density are inversely related at a given temperature and composition, thus making only the latter independent properties (temperature, molecular composition, and heat capacity ratio) important."

This sentence is confusing me, surely the heat capacity ratio is set by the molecular composition? For example (temperature and heat capacity ratio) would be ok, or (temperature and molecular composition) would be ok too, but having all three in there is seems wrong. Also, what's meant by "latter independent properties"? What makes them latter? Not edited myself because I'm not completely sure about it all.

I've tried to clarify. It's hard to say just what "molecular composition" means. For a pure gas with complex molecules at high temperatures (where vibration counts) what we want is the molecular formula, and indeed must have the structural formula, since n-pentane and tert-pentane have the same molecular formulas, but different structural formulas, and will different vibrational modes and thus heat capacities, and thus speeds of sound. You can in theory determine a gas heat capacity (and thus gamma) from just structural formulas (to give bending modes) and temperature, but it's a nasty problem in the heat capacity of gasses. Thus we cannot really say that temperature and molecular weight are the independent variables. That is true for monatomic gases, but for gases with complex molecules, the complexity must be taken account of, and simple molecular weight isn't enough to do it. Heat capacity (gamma) must either be given in addition to molecular weight for complex gas molecules, or else laboriously calculated ab initio from temperature and quantum mechanics. SBHarris 02:42, 30 August 2016 (UTC)

## Why does the beginning of this article state speeds and such using the Imperial system and then the SI units?

According to the Method of style of Wikipedia this article should be stating values using the metric units first.

Unit choice and order — Preceding unsigned comment added by 99.241.73.202 (talk) 22:54, 12 March 2016 (UTC)

Thank you for pointing this out - the order was changed only very recently. It seems clear that SI unit should have the priority on a global topic like this, and I have changed it back. (Manual of style, not "method" of style): Noyster (talk), 00:50, 13 March 2016 (UTC)

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## Units in the middle?

Perhaps there is good reason for it, but the 2nd and 3rd equations in section "Practical formula for dry air" place the m/s units in the middle of the right-hand-side of the equation which just looks weird to me. Aren't units conventionally placed at the end of an expression? It also almost looks like the radical is under the slant division line which I don't think is the intent. I think the m/s should be moved to the end of both of these equations.

You are right. It's been fixed now. SBHarris 00:10, 17 August 2016 (UTC)

Mtbusche (talk) 21:42, 16 August 2016 (UTC)