# Talk:Mach number

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## Pronunciation

I cannot fully agree to the below comments made to the pronounciation of the surname "Mach". During all my life, including my studies of aeronautics in Germany, I have never heard anybody pronouncing his name with a long "a". It is indeed to be pronounced like the german imperative of the 2nd person of "machen" ("do!"), which is with a short "a", like in the english word "duck". The "ch" at the end however is the bit that most non-german speakers will find most difficult to pronounce. It cannot be described in written form, but it is correct that it does not sound like "ck".

Regards from Germany, Christian —Preceding unsigned comment added by 195.124.114.36 (talk) 15:53, 12 August 2008 (UTC)

(Ernst) Mach is definitely pronounced like (Johann Sebastian) Bach, therefore {max}. "Mach" is also in German the imperative of "to do". "Mach etwas" means "do something".

But "Mach" (of Ernst) has got a long "a", and "Mach" in "Mach etwas" a short one. Other than that, I agree, it's like "Bach". "Mack" or "Mock" are nonsense. 80.75.192.71 08:38, 18 July 2007 (UTC)

Is Mach number really pronounced, as the article says, "mack" in British English and "mock" in American English? The reason I ask is that there has been some discussion on how Mach kernel is pronounced. In the discussion there (see Talk:Mach_kernel), some presume it is named after Austrian physicist Ernst Mach, and was pronounced the same as his name (like Bach). This would contradict to the information in this article about Mach number. So, the question really is, how is Ernst Mach pronounced (plus possible variants/alternatives)? Then, is Mach number named after his, yes or no? And if it is, is it pronounced like him or differently and why? And finally, is Mach kernel named after Ernst Mach and/or after Mach number and/or something else, and how and why is it pronounced (plus possible variants/alternatives)?

Mach is pronounced with Hard ch (IPA: [max]), same as J.S.Bach, it is named after Austrian physicist Ernst Mach, both are german names. Only some ignorant clod could use ill-sounding form like "mack". Why is it even mentioned in the article?? -- IEEE (talk) 02:29, 28 September 2008 (UTC)
Well, if you happen to speak a southern British dialect which doesn't use that [x] phoneme, it's usually much more comfortable to use "mack". Especially since with the long vowel you could confuse it with the word 'mark'. Either way, I agree that the pronunciation issue is irrelevant.--81.156.177.239 (talk) 21:11, 3 January 2009 (UTC)

## When an aircraft exceeds Mach 1...

When an aircraft exceeds Mach 1 a large pressure difference is created just in front of the aircraft. This pressure difference, called a shock wave, spreads backward and outward from the aircraft in a cone shape. It is this shock wave that causes the sonic boom heard as fast moving aircraft travels over head.

What was wrong with this paragraph, and how can it be fixed? AxelBoldt 00:27 Oct 3, 2002 (UTC)

Removed warp speed reference. It's not correct even in the ST universe. Roadrunner 17:58, 30 Mar 2004 (UTC)

## Overview

Can someone please de-confuse this section? what is it trying to say about how the speed corresponding to Mach-1 changes with height and temperature? We are told that an aircraft travelling at 20 deg. C travels at 86% of the speed compared to when it is at 11,000 metres and -50 deg. C. So what height is it at 20 deg. C? is that sea-level? How does the Mach-1 speed in metres/sec vary with different temperatures and heights? any ideas? someone must know :) — Preceding unsigned comment added by Historikeren (talkcontribs) 21:42, 26 February 2011 (UTC)

It seems more like a random fact than an overview and could be removed. The section previous to it appears to be the overview.Rmason81 (talk) 04:30, 13 January 2017 (UTC)
It's not random at all; it's based on how temperature is assumed to vary with altitude in the International Standard Atmosphere model. (The 20 deg. C was incorrect; standard sea level temperature is 15 deg. C.) I've tried to reorder it to make it clearer. JustinTime55 (talk) 16:09, 13 January 2017 (UTC)
What would really help to make it a lot clearer is if this page didn't keep secret the variation of sonic speed with absolute temperature:
${\displaystyle c_{\mathrm {ideal} }={\sqrt {\gamma \cdot R_{*}\cdot T}},}$ found in Speed of sound. JustinTime55 (talk) 16:25, 13 January 2017 (UTC)

## Speeds

Wanting opinions before making an edit I'm unsure of: Would it be beneficial to list, on the table, speeds (in kph, or mph, or m/s, or whatever) corresponding to each Mach number at typical temperatures and pressures? -FZ 22:21, 3 Aug 2004 (UTC)

I'm for creating a simple, small table of mach numbers at sea level and standard operational temperatures. If I were a middle or high school kid looking up mach numbers, I'd probably expect to find something like that on this page. --ABQCat 00:26, 1 Sep 2004 (UTC)
Ditto --Teradon 01:19, 27 April 2006 (UTC)

what happen to this? —Preceding unsigned comment added by 86.27.191.227 (talk) 14:37, 23 September 2008 (UTC)

## Images

I think that the images on this page are terrifically illuminating and valuable, but they are all taken from http://www.kurssit.lut.fi/040301000/main/11_3_2.html. User:Prkl75 added the images to Wikipedia and this article. There may be some copyright issues (despite the claim on the image pages), so if anyone happens to have some images that would work for this page in place of those aleady in use, I think that would be good. --ABQCat 00:50, 1 Sep 2004 (UTC)

The main image on the page is captioned "An F/A-18 Hornet breaking sound barrier". The caption implies that we can tell it is travelling supersonically from the visible condensation disc behind it. Other sources on the internet suggest this is an example of condensation from the Prandtl-Glauert singularity, and is not indicative of supersonic flow.JBel 16:11, 31 January 2007 (UTC)

The air flow diagrams are actually wrong because they depict the Equal transit-time fallacy. 142.103.207.10 (talk) 21:37, 8 February 2008 (UTC)

## I don't get it.

I don't understand. How are sound and the sonic boom effect related? Do sound waves have anything to do with this or are they unrelated?

This is partially addressed in the article, "When an aircraft exceeds Mach 1 (i.e. the sound barrier) a large pressure difference is created just in front of the aircraft. This abrupt pressure difference, called a shock wave, spreads backward and outward from the aircraft in a cone shape (a so-called Mach cone). It is this shock wave that causes the sonic boom heard as fast moving aircraft travels overhead...".
I think what could help any discussion here is if you were to ask a specific question which would potentially benefit the article through an explanation here and future inclusion into the article if needed. I think you may be looking more for an article such as "sonic boom" which has a less technical discussion of the phenomenon (some of which may actually benefit this article, if only to point non-technical readers to a more apropriate article for their inquiries). --ABQCat 19:54, 2 September 2005 (UTC)

## mach number and propagation of sound waves

How can one show the diagrams for the propagation of the sub-sonic, sonic and supersonic waves in form of their concentric circles formed and also their mach angle?

## Remove the PAF reference

Even though I'm Pakistani myself, I do not agree with putting the PAF page here. It does not contain generic information related to the unit of measure, and is a patriotic page. It does not belong here.

Link removed.
It was added again. I'll remove it, the link doesn't even work. Keta 21:17, 10 June 2006 (UTC)

High-speed flow around objects

High speed flight can be classified in five categories: can thee following info also put in brackets in addition like as follows:

   * Subsonic: Ma < 1
* Sonic: Ma = 1
* Transonic: 0.8 < Ma < 1.2 [0.8 Ma - 1.2 Mach]
* Supersonic: 1.2 < Ma < 5 [1.2 Ma - 5 Mach]
* Hypersonic: Ma > 5


Newbies and dummies like me find it easier this easier.

## Ernst Mach

was Czech...not Austrian...

That's not true. Ernst Mach was born in 1838 in a region which at that time belonged to the empire of Austria. Nonregarding the fact that that area NOW is part of the Tchech Republic, Ernst Mach was nevertheless of austrian nationality. He died in Munich, Germany.

Regards from Hamburg, Germany, Christian —Preceding unsigned comment added by 195.124.114.36 (talk) 15:05, 12 August 2008 (UTC)

Тhe current state jurisdiction of the city where he was born is not a reason to change his nationality. Its name is not even Czech, but German. And Republic of Czechoslovakia was formed in 1918 following the collapse of the Austro-Hungarian Empire, even after Mach's death (1916).Xunonotyk (talk) 10:09, 9 April 2019 (UTC)

## Speed of Sound depends on Pressure

In general, the speed of sound depends on the pressure of the medium. This is the main reason why the speed of sound decreases with increasing altitude. Of course, temperature also has an effect on pressure and thereby also affecting slightly the speed of sound. Didi7 12:04, 18 January 2007 (UTC)

According to the Speed of sound article you have this backwards. The temperature is the important quantity. "Air pressure has no effect at all in an ideal gas approximation." Spiel496 21:41, 27 January 2007 (UTC)

So density of material is important, but pressure within that material is not? One would think that the closer the molecules are, the faster a wave can travel through it. —Preceding unsigned comment added by 87.186.72.98 (talk) 09:39, 22 January 2011 (UTC)

Assuming the medium in question is (or at least is modelled as) a perfect gas, the speed of sound is independent of pressure. Increasing pressure does increase the 'elasticity' of the gas, but it equally increases the density. Since the speed of sound is governed by the relative variation of these properties, the effect of pressure is 'self cancelling' - the only way to alter pressure independently of density is to alter the temperature.80.229.172.13 (talk) 16:46, 20 December 2011 (UTC)

## Mach speed decreases with altitude?

If actual speed at Mach 1 increases with altitude, why do the numbers in the overview decrease? BQZip01 18:31, 27 February 2007 (UTC)

Huh? 'Mach 1 increases with altitude', where does the article say that? Temperature goes down with altitude.WolfKeeper 18:43, 27 February 2007 (UTC)
The temperature drops, but the air density does too. As for the reference "So, an aircraft travelling at Mach 1 at sea level (340.3 m/s, 1,225.08 km/h) will experience shock waves in much the same manner as when it is travelling at Mach 1 at 11,000 m (36,000 ft), even though it is travelling at 295 m/s (654.632 MPH, 1,062 km/h, 86% of its speed at sea level)." If this were the case, aircraft would fly lower to fly faster (which makes precious little sense). P.S. please don't take this as criticism, I just am confused. It may be one of those things that is counterintuitive BQZip01 18:54, 27 February 2007 (UTC)
Still awaiting an answer on this one BQZip01 14:59, 14 March 2007 (UTC)
Mach number is just a number that describes some aspect of the flow around the vehicle. The vehicles in general are trying to minimise drag for the speed that they are travelling at. This in general can be done at an optimum altitude for the current vehicle mass/weight, which varies over the length of the flight. As the vehicle weight goes down, the vehicle's ballistic coefficient is reduced and the vehicle needs to fly higher to maintain the same fuel efficiency over the ground. At low altitude the mach number would be the same or lower as at higher altitude, but the air drag would be much higher as well, so the fuel economy would suffer.WolfKeeper 02:12, 18 March 2007 (UTC)

## LEO Mach

Is it correct to say "(For comparison: the required speed for low Earth orbit is ca. 7.5 km·s-1 = Ma 25.4 in air at high altitudes)"? Agnamus (talk) 12:25, 1 July 2008 (UTC)

Not really. Most, if not all treatments of the speed of sound, mach number, fluid dynamics, etc. are (at least in this article) based on modelling fluids as a continuum - by the time (altitude) you get to low earth orbit, the molecules are so far apart, the Mach number is more or less meaningless. See Knudsen number. I'm not 100% sure about this, but I'm almost certain that it is the case (?) 80.229.172.13 (talk) 17:41, 20 December 2011 (UTC)

## increment

what is the increment between each mach speed? is Mach 2 twice the speed of sound? —Preceding unsigned comment added by 86.27.191.227 (talk) 14:39, 23 September 2008 (UTC)

If a body is moving at true airspeed V in a gas, and the temperature of the gas in the vicinity of the body is T, then the Mach number of the body is V divided by the speed of sound in the gas at temperature T. If the body is moving at Mach 2 it is moving at twice the speed of sound; if it is moving at X times the speed of sound it is moving at Mach X. Apologies for the delay in providing an answer to your question. Dolphin51 (talk) 10:46, 4 January 2009 (UTC)

sorry to piggyback on this guys thing but my question is what is the highest mach we have gotten up to?Mail me at qanda666@yahoo.com —Preceding unsigned comment added by 75.12.165.254 (talk) 23:05, 10 February 2009 (UTC)

## Critical Mach Number

Explanation / definition of 'critical mach number' of subsonic aircraft, please. GilesW (talk) 14:54, 5 June 2009 (UTC)

The Critical Mach number refers to the speed at which loss of control of the aircraft is evident, i.e., moving the control(s) - usually the elevator - has no effect. The slightly lower Mach number at which a subsonic aircraft is still capable of useful maneuvering, i.e., in combat, is called the Tactical Mach number. —Preceding unsigned comment added by 213.40.254.30 (talk) 18:23, 5 September 2009 (UTC)
Don't you think there should be some explanation on the article then. 'Mcrit' is written with no explanation for what it is and I still don't fully understand. Officially Mr X (talk) 10:39, 15 February 2010 (UTC)
Perhaps the simplest explanation for a layman is this: As an aeroplane approaches the speed of sound, Mach 1, the compression of the air (due to the aeroplane moving through it) creates shock waves that buffet the aircraft. Then, as the speed increases further, the effect of the shock waves is to move the centre of pressure (lift) backwards towards the tail, changing the balance of the aircraft so that it becomes nose-heavy, and wants to dive. To counteract this, the pilot must pull back on the control column to raise the elevators and prevent the nose from dropping. As speed increases still further, there comes a point where the pilot can no longer hold the nose of the aeroplane up, and the aircraft then starts to do what is called a 'bunt' - a downwards half-loop. It is at around this point where the pilot can no longer stop the nose from dropping that the Critical Mach Number is usually measured.
In the days of the last piston-engined fighters and the first jet fighters these sorts of speeds were only capable of being reached in a dive, and with the controls all manually operated, a pilot's physical strength had a degree of bearing on when he could no longer prevent the nose from dropping below the intended flight path (i.e., steepening the dive), hence a strong pilot would be able to endure a higher speed in a dive compared to a physically weaker pilot. So the Mcrit is not really a fixed figure for these aircraft, it's more of a guideline and is usually based on the abilities of the 'average' service pilot. The problem here of course, is that the aeroplane is already diving, so that any steepening of the dive actually increases the airspeed due to the effects of gravity. When this happens the pilot is faced not only with a loss of control, but with a steadily worsening strain on the airframe, which may well cause it to break up. The only good point about these dives was that as the aircraft descended to lower altitudes, the air was warmer and the speed of sound (Mach 1) rose relative to airspeed, so that eventually the shock waves dissipated - the speed of sound in air is lower the higher you fly - it's about 660 knots at sea level. This was the problem that was known in aviation circles in the late 1930s/1940s as the Sound Barrier. Transonic and supersonic aircraft don't have a Critical Mach Number, as they are expressly designed to be able to be controlled at and above the speed of sound.
Incidently, this backwards-moving of the 'balance' of the aeroplane occurs in all aircraft that go through the 'sound barrier' and in the case of the Concorde supersonic airliner, the balance of the aeroplane was maintained by pumping fuel from tanks at the front of the aircraft to tanks at the rear when going supersonic. This procedure was then reversed when slowing down to below the speed of sound. —Preceding unsigned comment added by 86.112.53.227 (talk) 13:15, 27 February 2011 (UTC)

## Speed of sound is dependent on the density of the fluid, not its temperature

The article claims that the speed of sound is solely dependent on ambient air temperature. This is inaccurate. The higher the density of the fluid (in this case, a gas) the more condensed its atoms become - hence increasing the rate at which sound can propagate through the medium. Whilst temperature does have a direct effect on density, it also has an effect on pressure. According to the Ideal gas law, we can surmise that pV = nRT - where P = Pressure V = Volume, n = number of molecules (mole) R = gas constant and T = temperature. By transposing the formula to n = pV.RT, we can see that temperature, gas constant, pressure and volume all determine the density of the fluid. The higher the value of n, the more molecules per unit of V. —Preceding unsigned comment added by 211.27.67.61 (talk) 11:16, 16 October 2010 (UTC)

I think you are overstating the case. The speed of sound can be expressed in a number of different ways. Speed of sound shows that it can be expressed as follows:
1. ${\displaystyle c={\sqrt {\tfrac {K}{\rho }}}\,}$
Expression 1. permits us to say the speed of sound is a function of the bulk modulus K of the medium, and the density of the medium.

2. ${\displaystyle c^{2}={\frac {\partial p}{\partial \rho }}}$
Expression 2. permits us to say the speed of sound is a function of the rate of change of pressure with respect to density.

3. ${\displaystyle c_{\mathrm {ideal} }={\sqrt {\gamma \cdot R\cdot T \over M}}={\sqrt {\gamma \cdot k\cdot T \over m}}\,}$

Expressions 3. permit us to say that, for a given medium, the speed of sound is solely a function of the absolute temperature.

You are correct in saying the speed of sound can be expressed as a function of density (and also the bulk modulus.) However, none of the above expressions permit us to say the speed of sound can only be expressed correctly in one way, and all other ways are incorrect. Therefore you are incorrect in saying the speed of sound cannot be expressed solely as a function of temperature.

In aviation, it is common for people to ask about the speed of sound at a particular pressure altitude. The best reply is to say the speed of sound is related to the ambient air temperature, but is not related to the air pressure (or the pressure altitude), or the air density (or density altitude.) Dolphin (t) 11:58, 16 October 2010 (UTC)

It is true that the speed of sound is a function of bulk modulus and the reciprocal of density:
${\displaystyle c={\sqrt {\tfrac {K}{\rho }}}\,}$
However, Bulk modulus#Thermodynamic relation shows that bulk modulus is a function of pressure:
${\displaystyle K_{s}=\gamma P}$
Therefore it is accurate to state that the speed of sound is a function of pressure and the reciprocal of density, and this can be expressed in the following formula:
${\displaystyle c={\sqrt {\tfrac {\gamma P}{\rho }}}}$
But the equation of state ${\displaystyle P=\rho RT}$ allows us to transform the speed of sound to:
${\displaystyle c={\sqrt {\gamma RT}}}$
which shows the speed of sound for a given medium (such as air) is a function of temperature only.
All this shows the speed of sound is a function of any of the following:
• bulk modulus and the reciprocal of density
• pressure and the reciprocal of density
• temperature
Hence the accuracy of the statement in the article that the speed of sound in air is solely dependent on air temperature. Dolphin (t) 01:39, 19 October 2010 (UTC)

## Could someone savvy add a CHART/TABLE of speeds for each Mach number?

It would be great to have a CHART/TABLE that lists speeds for each Mach number.

For Example:

Mach1 = MPH | KmH | Knots | Whatever

Mach2 = MPH | KmH | Knots | Whatever

Mach3 = MPH | KmH | Knots | Whatever

Mach4 = MPH | KmH | Knots | Whatever

Mach5 = MPH | KmH | Knots | Whatever

Mach6 = MPH | KmH | Knots | Whatever

...

Mach881,000* (the supposed speed of light) = MPH | KmH | Knots | Whatever.

Please? Thank you!

Misty MH (talk) 00:38, 8 September 2011 (UTC)

Misty, the problem is that the speed of sound varies quite a bit with pressure altitude, tempreature, etc. However, if someone could come up with numbers for a "standard" day (Sea level, 29.92" mercury, 59°F (15°C)), that might be a somewhat useful form of comparison. We could also go with just some set parameters and show a disclaimer stating what the parameters were. Here's a calculator you can use to fiure out the numbers and add it yourself! Buffs (talk) 02:42, 8 September 2011 (UTC)
Thanks Buffs.
I actually thought there was something like that standard-day idea; or maybe it was in a related W. article.
Misty MH (talk) 00:32, 11 September 2011 (UTC)
Buffs is correct on a couple of points, but incorrect when he suggests the speed of sound varies with pressure altitude, and misleading when he suggests we could come up with numbers for a standard day. The speed of sound in air varies only with temperature. Regardless of the altitude, or pressure altitude, or whether it is a standard day or not, once we know the temperature of the air we can determine the speed of sound in that air with a high level accuracy.
The formula for the speed of sound a in a gas is:
${\displaystyle a={\sqrt {\gamma RT}}}$ where γ is the heat capacity ratio for the gas, R is the specific gas constant for the gas, and T is the temperature of the gas in Kelvin.
For example, in air at 15°C (288K) the speed of sound is 661.5 knots, 1116.4 ft.s-1, 761.2 mi.hr-1, 340.3 m.s-1, 1 225 km.hr-1, regardless of whether this air at 15°C is at sea level or some other altitude. See Speed of sound#Tables. Dolphin (t) 06:09, 11 September 2011 (UTC)

## Which standard?

"At Standard Sea Level conditions (corresponding to a temperature of 15 degrees Celsius), the speed of sound is 340.3 m/s (1225 km/h, or 761.2 mph, or 661.5 knots, or 1116 ft/s) in the Earth's atmosphere. The speed represented by Mach 1 is not a constant; for example, it is mostly dependent on temperature Standard Sea Level conditions (corresponding to a temperature of 15 degrees Celsius), the speed of sound is 340.3 m/s (1225 km/h, or 761.2 mph, or 661.5 knots, or 1116 ft/s) in the Earth's atmosphere. The speed represented by Mach 1 is not a constant; for example, it is mostly dependent on temperature." Thnidu (talk) 00:51, 10 July 2015 (UTC)

That would be the International Standard Atmosphere. JustinTime55 (talk) 17:35, 12 January 2017 (UTC)

## External links modified

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## Plural or singular?

"compressibility effects will be small and a simplified incompressible flow equations can be used"

Is it plural or singular?

Aisteco (talk) 20:10, 11 January 2017 (UTC)

Plural, unless proven otherwise. Andy Dingley (talk) 21:11, 11 January 2017 (UTC)