Talk:Speed of sound

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1 In MPH/KPH
2 Terminology
3 Linear with temperature?
4 Speed of sound = speed of movement of 'pressure'?
5 and humidity
6 Relativistic effects
7 Pressure
8 Sound in solids
9 Experiments to measure the speed of sound
10 Universal gas constant
11 Problem with the pressure statement (and speed is 331.6, not 331.5)
12 Basic concept
13 331.6 m/s
14 Speed of sound in solid
15 Speed in a liquid

[edit] In MPH/KPH

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_air — Omegatron 22:58, 20 February 2006 (UTC)

Taking the speed of sound as 331.6 m/s, then it would be very roughly 1194 km/h (rounding to the nearest unit), which would be roughly 740 MPH (rounding to the nearest five units. I hope this is accurate enough for your needs. — NRen2k5 7:47, 15 August 2006

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

[edit] 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

[edit] 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...

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

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). S B H arris 18:06, 11 July 2006 (UTC)

[edit] Speed of sound = speed of movement of 'pressure'?

mighte 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, one could accuratly 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.S B H arris 18:11, 11 July 2006 (UTC)

[edit] and humidity

(William M. Connolley 20:48, 16 Oct 2004 (UTC)) The article says:

The humidity has very little effect on the speed of sound, while the static sound pressure (air pressure) has none. Sound travels slower with an increased altitude (elevation if you are on solid earth), primarily as a result of temperature and humidity changes.

So does humidity matter, or not?

The contribution from humidity is small compared to the contribution from temperature.

The contribution of humidity is small comnpared to temperature, but still significant. By treating air and water vapor as ideal gases and calculating the properties of the mixture, you can determine that as humidity increases, density decreases, the average molar mass decreases and gamma decreases. The calculation is not trivial, but neither is it complex. Since the partial pressure of water vapor increases with temperature, the effect of humidity increases with temperature. The difference in sound speed between dry and saturated air at 0C is about 0.3 m/s, the difference at 30 degrees C is about 2 m/s. This is certainly more significant than the 331.3 vs. 331.6 quibbling below. The result of an increase in humidity is an increase in sound speed.--Ron E 18:42, 25 February 2007 (UTC)

[edit] 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)

[edit] 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.

[edit] 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)

[edit] 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)

[edit] 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)

[edit] 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]

[edit] 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)

[edit] 331.6 m/s

Should we use the speed of sound for 0 °C as 331.5 or 331.6 m/s?
Google shows 829 answers for 331.6:
http://www.google.com/search?&q=Speed+of+sound 331.6
Google shows 11,500 answers for 331.5
http://www.google.com/search?&q=Speed+of+sound 331.5
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. S B H arris 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. S B H arris 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. S B H arris 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)

[edit] Speed of sound in solid

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

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

where

E is Young's modulus

ρ

(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).

$\sqrt{\frac{Pa}{kg/m^3}} = \sqrt{\frac{N/m^2}{kg/m^3}} =\sqrt{\frac{(kg*m/sec^2)/m^2}{kg/m^3}} = \sqrt{\frac{m^2}{sec^2}} = \frac{m}{s}$

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. S B H arris 16:31, 21 January 2007 (UTC)

[edit] 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. S B H arris 21:32, 23 January 2007 (UTC)

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