#### [SOLVED] What is the speed of sound in space?

Given that space is not a perfect vacuum, what is the speed of sound therein? Google was not very helpful in this regard, as the only answer I found was $300\,{\rm km}\,{\rm s}^{-1}$, from Astronomy Cafe, which is not a source I'd be willing to cite.

#### @pela 2015-01-29 12:59:02

By popular demand (considering two to be popular — thanks @Rod Vance and @Love Learning), I'll expand a bit on my comment to @Kieran Hunt's answer:

## Thermal equilibrium

As I said in the comment, the notion of sound in space plays a very significant role in cosmology: When the Universe was very young, dark matter, normal ("baryonic") matter, and light (photons) was in thermal equilibrium, i.e. they shared the same (average) energy per particle, or temperature. This temperature was so high, that neutral atoms couldn't form; any electron caught by a proton would soon be knocked off by a photon (or another particle). The photons themselves couldn't travel very far, before hitting a free electron.

## Speed of sound in the primordial soup

Everything was very smooth, no galaxies or anything like that had formed. Stuff was still slightly clumpy, though, and the clumps grew in size due to gravity. But as a clump grows, pressure from baryons and photons increase, counteracting the collapse, and pushing baryons and photons outwards, while the dark matter tends to stay at the center of the overdensity, since it doesn't care about pressure. This creates oscillations, or sound waves with tremendously long wavelengths.

For a photon gas, the speed of sound is $$\begin{array}{rcl} c_\mathrm{s} & = & \sqrt{p/\rho} \\ & = & \sqrt{c^2/3} \\ & \simeq & 0.58c, \end{array}$$ where $$c$$ is the speed of light, and $$p$$ and $$\rho$$ are the pressure and density of the gas. In other words, the speed of sound at that time was more than half the speed of light (for high temperatures there is a small correction to this of order $$10^{-5}$$; Partovi 1994).

In a non-relativistic medium, the speed of sound is $$c_\mathrm{s} = \sqrt{\partial p / \partial \rho}$$, which for an ideal gas reduces to the formula given by @Kieran Hunt. Although in outer space both $$p$$ and $$\rho$$ are extremely small, there $$are$$ particles and hence it odes make sense to talk about speed of sound in space. Depending on the environment, it typically evaluates to many kilometers per second (i.e. much higher than on Earth, but much, much smaller than in the early Universe).

## Recombination and decoupling

As the Universe expanded, it gradually cooled down. At an age of roughly 200,000 years it had reached a temperature of ~4000 K, and protons and electrons started being able to combine to form neutral atoms without immediately being ionized again. This is called the "Epoch of Recombination", though they hadn't previously been combined.

At ~380,000 years, when the temperature was ~3000 K, most of the Universe was neutral. With the free electrons gone, photons could now stream freely, diffusing away and relieving the overdensity of its pressure. The photons are said to decouple from the baryons.

## Cosmic microwave background

The radiation that decoupled has ever since redshifted due to the expansion of the Universe, and since the Universe has now expanded ~1100 times, we see the light (called the cosmic microwave background, or CMB) not with a temperature of 3000 K (which was the temperature of the Universe at the time of decoupling), but a temperature of (3000 K)/1100 = 2.73 K, which is the temperature that @Kieran Hunt refers to in his answer.

## Baryon acoustic oscillations

These overdensities, or baryon acoustic oscillations (BAOs), exist on much larger scales than galaxies, but galaxies tend to clump on these scales, which has ever since expanded and now has a characteristic scale of ~100 $$h^{-1}$$Mpc, or 465 million lightyears. Measuring how the inter-clump distance change with time provides a way of understanding the expansion history, and acceleration, of the Universe, independent of other methods such as supernovae and the CMB. And beautifully, the methods all agree.

#### @F. Ha 2016-02-28 15:30:51

slightly off-topic, but I feel that I have to take a course in astroparticle-physics :)

#### @pela 2016-02-28 16:28:39

Don't we all… :) Do you mean in order to understand the answer, or just in general?

#### @honeste_vivere 2015-04-29 12:58:07

I know this question is technically already answered, but there were several things missing from the answers that I thought should be mentioned (I am writing a review paper comparing different regions of space so I had these numbers at hand already as well).

The speed of sound in space has multiple meanings because space is not a vacuum (though the number density of Earth's magnetosphere can be ~6-12 orders of magnitude more tenuous than the best vacuums produced in labs), it is full of ionized particles, neutral and charged dust.

In the interplanetary medium or IPM, there are five relevant speeds that can all be considered a type of sound in a way, because each are related to the speed of information transfer in the medium.

# Classical idea of sound speed

When one discusses the speed of sound, they generally refer to the common form of $C_{s}^{2} = \partial P/\partial \rho$, where $P$ is the thermal pressure and $\rho$ is the mass density. In a plasma, this takes the slightly altered form of: $$C_{s}^{2} = \frac{ k_{B} \left( Z_{i} \ \gamma_{e} \ T_{e} + \gamma_{i} \ T_{i} \right) }{ m_{i} + m_{e} }$$ where $k_{B}$ is Boltzmann's constant, $Z_{s}$ is the charge state of species $s$, $\gamma_{s}$ is the adiabatic or polytrope index of species $s$, $m_{i}$ is the mass of species $s$, and $T_{s}$ is the average temperature of species $s$. In a tenuous plasma, like that found in the IPM, it is often assumed that $\gamma_{e}$ = 1 (i.e., isothermal) and $\gamma_{e}$ = 2 or 3, or that $\gamma_{e}$ = 1 and $T_{e} \gg T_{i}$. The above form of the sound speed is known as the ion-acoustic sound speed because it is the phase speed at which linear ion-acoustic waves propagate. Thus, $C_{s}$ is a legitimate type of sound speed in space.

In the IPM, $C_{s}$ ~ 13 - 240 km/s [e.g., Refs. 12; 33; 34].

# Speed of magnetic fields

The cryptic title is eluding to what is known as the Alfvén speed, which is defined as: $$V_{A} = \frac{ B_{o} }{ \sqrt{ \mu_{o} \ \rho } }$$ where $B_{o}$ is the magnitude of quasi-static, ambient magnetic field, $\mu_{o}$ is the permeability of free space, and $\rho$ is the plasma mass density (which is roughly equivalent to the ion mass density unless it's a pair plasma). This speed is typically associated with transverse Alfvén waves, but the speed is relevant to information transfer in plasmas, thus why I included it here.

In the IPM, $V_{A}$ ~ 4 - 220 km/s [e.g., Refs. 10; 12; 33; 34].

# Speed of magnetized sound waves

In a magnetized fluid like a plasma, there are fluctuations that are compressive whereby they compress the magnetic field in phase with the density. These are known as magnetosonic or fast mode waves. The full MHD definition of the phase speed for a fast mode wave is given by: $$2 \ V_{f}^{2} = \left( C_{s}^{2} + V_{A}^{2} \right) + \sqrt{ \left( C_{s}^{2} + V_{A}^{2} \right)^{2} + 4 \ C_{s}^{2} \ V_{A}^{2} \ \sin^{2}{\theta} }$$ where $\theta$ is the angle of propagation with respect to $\mathbf{B}_{o}$. $V_{f}$ is the relevant speed for shock waves in weakly collisional and collisionless plasmas. It is also a type of sound speed, thus the name magnetosonic.

In the IPM, $V_{f}$ ~ 17 - 300 km/s [e.g., Refs. 10; 12; 33; 34].

Side Note
There is also a slow mode wave, which differs in polarization and the relative phase between the magnetic and density fluctuations. It is called slow because it has a smaller phase speed than the fast mode in the same medium.

# Thermal speeds

The last two speeds that are relevant are the thermal speeds of the electrons and ions. The one-dimensional rms speed is given by: $$V_{Ts}^{rms} = \sqrt{\frac{ k_{B} \ T_{s} }{ m_{s} }}$$ where the definitions are the same as in previous sections and $s$ can be $e$(electrons) or $i$(ions). Generally we use the three dimensional most probable speed, which is given by: $$V_{Ts}^{mps} = \sqrt{\frac{ 2 \ k_{B} \ T_{s} }{ m_{s} }}$$

In the IPM, the electron [e.g., Refs. 2; 3; 5; 7; 8; 14; 17-22; 24; 25; 27; 29-34] and ion [e.g., Refs. 1-6; 8-11; 13; 15-17; 19; 20; 23; 26-32] thermal speeds are $V_{Te}^{mps}$ ~ 1020 - 5170 km/s and $V_{Ti}^{mps}$ ~ 13 - 155 km/s, respectively.

# Summary

There are several different types of sound-like speeds in space and each of them can produce similarly related phenomena. For instance, we often refer to Mach numbers associated with $C_{s}$, $V_{A}$, and $V_{f}$. In addition, there are several plasma instabilities that result from an effect that similar to Cerenkov radiation, whereby a beam of particle exceeds, for instance, the electron thermal speed.

In summary, in the regions outside of local magnetospheres but within the realm of our sun's influence, there is a wide range of sound speeds.

# Update

A paper on the statistics of temperature-dependent parameters near Earth in the solar wind was recently published in Astrophys. J. Suppl. by Wilson et al. [2018] (it's Open Access so no paywall). The work provides new measurements but also provides a detailed literature review/reference list of past work.

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#### @CoolHandLouis 2016-12-19 18:31:23

Please update with a highlighted cite to the review paper. Thanks!

#### @honeste_vivere 2016-12-19 20:44:54

@CoolHandLouis - Unfortunately, I am still waiting on several of my co-authors to contribute their chapters to the review and they are being slow about it (some were teaching and others were moving from one university to another which added delays).

#### @mmesser314 2016-02-28 14:50:50

Direct measurement shows the speed is 1100 m/s.

ESA's dart-like Gravity field and Ocean Circulation Explorer (GOCE) Earth Explorer used to orbit as close to Earth as possible - just 260 km up - to maximize its sensitivity to variations in Earth's gravity field. At that altitude, there is enough atmosphere to exert a small drag. The satellite had an aerodynamic shape and a small engine to keep it in orbit. The mission ended when the engine ran out of fuel.

In 2011, the huge 9.1 Japanese Tohoku earthquake generated atmospheric disturbances. These deflected the satellite. Density variations were also measured. Article and video here.

#### @honeste_vivere 2016-03-19 13:18:51

This is very interesting and I would like to learn more but I do not think this addresses the OP.

#### @mmesser314 2016-03-19 15:11:12

@honeste_vivere - I guess it depends on which region of space interests him. If space starts at an arbitrary altitude of 100 km, then this counts. But the density certainly is higher here than most places. Your answer is better.

#### @honeste_vivere 2016-03-20 15:13:41

I was more referring to the fact that a distortion in the atmosphere is not a "speed of sound." The speed at which the distortion propagates is the speed of sound, but that would change with altitude.

#### @mmesser314 2016-03-20 23:19:44

@honeste_vivere - I do not understand the distinction you are making. It seems to me that the distortion propagates at the speed of sound, and the speed is inferred from the time it takes to get from the ground to the satellite. Perhaps they modeled the speed as a function of altitude and scaled the expected speeds to fit the elapsed time. Am I missing something?

#### @honeste_vivere 2016-03-21 13:23:10

It's that the tsunami physically displaced a large amount of water which then displaced air, much like wind. Wind is not a sound wave. The displacement propagated near the speed of sound most likely because the initial displacement occurred so quickly (kind of like a short duration impact). From your figure, it does appear that they accounted for the variation in sound speed with altitude, but a bulging atmosphere due to displacement is a bulk flow of a fluid, not a longitudinal oscillation that propagates. Does that make more sense?

#### @honeste_vivere 2016-03-22 12:23:06

Ah I see... yes, that is okay.

#### @Kyle Oman 2015-01-29 18:38:08

Just want to bring up that most answers seem to be taking "space" to be a nice uniform medium. However, even within our own galaxy, conditions vary wildly. Here are the most common environments in the Milky Way:

• Molecular Clouds, $\rho\sim 10^4\,{\rm atom}/{\rm cm}^3$, $T\sim 10\,{\rm K}$
• Cold Neutral Medium, $\rho\sim 20\,{\rm atom}/{\rm cm}^3$, $T\sim 100\,{\rm K}$
• Warm Neutral Medium, $\rho\sim 0.5\,{\rm atom}/{\rm cm}^3$, $T\sim 10^4\,{\rm K}$
• Warm Ionized Medium, $\rho\sim 0.5\,{\rm atom}/{\rm cm}^3$, $T\sim 8000\,{\rm K}$
• HII Region, $\rho\sim 1000\,{\rm atom}/{\rm cm}^3$, $T\sim 8000\,{\rm K}$
• Hot Ionized Medium, $\rho\sim 10^{-3}\,{\rm atom}/{\rm cm}^3$, $T\sim \;{>}10^6\,{\rm K}$

The sound speed is proportional to $\sqrt{T}$. Given that the temperature varies over about 7 orders of magnitude (maximum at about $10^7\,{\rm K}$, minimum at about $3\,{\rm K}$), the sound speed varies by at least a factor of $1000$. The sound speed in a warm region is on the order of $10\,{\rm km}/{\rm s}$.

Trivia: the sound speed plays a crucial role in many astrophysical processes. This speed defines the time it takes for a pressure wave to propagate a given distance. One place this is a key time scale is in gravitational collapse. If the sound crossing time for a gas cloud exceeds the gravitational free fall time (time for a gravity-driven disturbance to propagate), pressure is unable to resist gravitational collapse and the cloud is headed toward the creation of a more compact object (denser cloud, or if conditions are right, a star).

More trivia: space is a very poor carrier (non carrier) of high frequency sounds because the highest frequency pressure wave that can be transmitted has a wavelength of about the mean free path (MFP) of gas particles. The MFP in space is large, so the frequency limit is low.

#### @David Hammen 2015-01-30 12:04:25

+1. This is the answer to this question. The hot intracluster medium can be even hotter than the items on your list, up to $10^8$ kelvin. A high metallicity molecular cloud is not ionized and can contain some fairly massive compounds. You can easily add another order of magnitude to that factor of 1000.

#### @supercat 2015-01-30 18:10:39

Even though sound travels faster in space than in a terrestrial atmosphere, the vacuum of space isn't generally regarded as carrying sound well. Is that because pressure waves in space will be primarily reflected when they hit solid objects, or because they'll be converted to heat when they hit solid objects, or because they get converted to heat in transit?

#### @Kyle Oman 2015-01-30 19:34:38

@supercat What solid objects? Space is very empty, on average! Space is a very poor carrier (non carrier) of high frequency sounds because the highest frequency pressure wave that can be transmitted has a wavelength of ~the mean free path of gas particles. The MFP in space is large, so the frequency limit is LOW.

#### @supercat 2015-01-30 19:54:43

I was referring to the idea that someone in a spacecraft isn't likely to hear much noise from outside. What you're saying is that even though the speed of sound is higher, it's nowhere near enough higher to make any audio frequency sounds meaningful given the wide spacing of the particles involved?

#### @Kyle Oman 2015-01-30 20:21:50

@supercat you're confusing two things here. Speed of sounds is one thing. Frequencies that can be carried by a fluid is another. The frequencies that can be carried by the ISM are much lower than the lower limit of human hearing. That doesn't mean the sounds aren't meaningful, or that they don't exist. They just have low frequencies.

#### @hobbs 2015-01-31 05:55:23

@supercat it's due to the low acoustic impedance of space -- it's not so much that space is bad at carrying sound, but that it's hard to transfer sound from an object into space and vice versa. With such a low density, the amount of energy that the interstellar medium can absorb from a vibrating object, or impart to another object, is very low. There just aren't the atoms for it, even if the temperature (and thus speed of sound) is fairly high.

#### @hobbs 2015-01-31 06:01:53

A perfectly elastic running fork in space would keep vibrating for much longer than one in atmosphere, because the surroundings would carry its energy away much more slowly. But it's that carrying away of energy that constitutes the transmission of sound.

#### @peterh 2015-01-31 11:06:41

+1, wonderful answer. What I don't understand: the hot neutral medium is hotter as the hot ionized medium?

#### @supercat 2015-01-31 16:45:57

@hobbs: As Kyle reminded me, the concept of "impedance" in a sound-transmission medium is only meaningful at frequencies which are low relative to the frequency of particle interactions. For a tuning fork vibrating at 440Hz to transmit any meaningful information about its frequency, it must be hit by a lot more than 440 particles per second [regular sampling at 880 would suffice; I'm not sure how to describe the information conveyed by random samples].

#### @Kyle Oman 2015-01-31 18:58:56

@PeterHorvath can't say that astronomers are particularly good at terminology :/

#### @Kieran Hunt 2015-01-29 09:17:06

From the ideal gas law, we know: $$v_\textrm{sound} = \sqrt{\frac{\gamma k_\textrm{B} T}{m}}$$ Assuming that interstellar space is heated uniformly by the CMB, it will have a temperature of $2.73\textrm{K}$. We know that most of this medium comprises protons and neutral hydrogen atoms at a density of about 1 atom/cc. This means that $\gamma = 5/3$, and $m = 1.66\times 10^{-27}\textrm{kg}$, giving a value for $v_\textrm{sound}$ of $192\textrm{m s}^{-1}$.

However, this is not propagated efficiently in a vacuum. In the extremely high vacuum of outer space, the mean free path is millions of kilometres, so any particle lucky enough* to be in contact with the sound producing object would have to travel light-seconds before being able to impart that information in a secondary collision.

*Which for the density given, would only be about 50 hydrogen atoms if you clapped your hands - very low sound power!

-Edit- As has quite rightly been pointed out in the comments, the interstellar medium is not that cold. At the moment, our solar system is moving through a cloud of gas at approximately 6000K. At this temperature, the speed of sound would be approximately $9000\textrm{m s}^{-1}$.

See Kyle's answer for a table of values for $v_\textrm{sound}$ that can be found in different environments in space, or pela's for information on how early universe sound waves became responsible for modern-day large scale structure.

#### @pela 2015-01-29 09:33:00

Argh, you beat it to me by seconds. Well, let me just add that sound in space plays a very significant role in cosmology: Just before recombination, 380.000 years after Big Bang, the speed of sound was approximately half the speed of light. When light and matter decoupled, the sound waves remained "frozen" in space, meaning that galaxies tend to form in clumps that are separated by this wavelength. The distance between these clumps expands with the general expansion of the Universe (and is now ~465 million lightyears), and provides a standard measure of length.

#### @mattecapu 2015-01-29 10:10:01

@pela wow that's really cool

#### @David Hammen 2015-01-29 10:46:39

-1. This is not a good answer. Nothing in space is that cold. The interplanetary medium is in the tens of thousands of kelvins. The interstellar medium varies from ten of kelvin in molecular clouds to tens of millions of kelvins. The intergalactic medium is extremely hot, again in the tens of millions of kelvins. The widely varying temperature and makeup (molecular hydrogen vs ionized plasma) means the speed of sound in space varies considerably.

#### @Kieran Hunt 2015-01-29 10:55:26

I've updated it for the ISM the solar system is currently passing through - my bad though, I hadn't really thought through the processes that generate it, just that it was there and in equilibrium with the CMB.

#### @WetSavannaAnimal 2015-01-29 11:01:08

@pela I think there's some stuff there that would be well worth expanding on and making your own answer adding to Kieran's - especially given your background.

#### @algiogia 2015-01-29 13:47:19

I suppose 6000K is the AVERAGE temperature, otherwise we would be boiling...

#### @JohannesD 2015-01-30 08:51:54

@algiogia: No. Temperature is not what matters, heat is. A gas cloud that sparse has negligible total heat energy even if the individual molecules are pretty energetic.

#### @yo' 2015-01-30 08:52:51

@DavidHammen Either you are completely right (with no buts) and then I don't see why Earth is not melted. Or there's a but, like "but there's chemical loss of heat energy" or "but there's radiation loss of heat energy" or whatever.

#### @yo' 2015-01-30 08:53:38

@JohannesD Well, the Earth is here for 5 billion years, pretty enough time to get heated even by the vacuum, if all around you is at 6kK.

#### @Svalorzen 2015-01-30 11:07:22

@yo' He is right. You can see it very simply in this way: what happens if you drop a blazing hot metal ball in the sea? The sea does not boil. To go back to reality, the ball is space: very hot, but with very low mass (very few atoms around). The Earth then is the sea: low temperature, but huge. Thus Earth is not boiling.

#### @David Hammen 2015-01-30 14:53:21

@yo' - The "but" is very simple. The medium may well be very hot, BUT because it's so very, very tenuous, there is hardly any heat transfer from it to a macroscopic object. For a macroscopic object in space, radiative heat transfer (heat from the sun, cooling toward empty space) completely dominates over heat transfer from the hot but almost non-existent medium.

#### @yo' 2015-01-30 15:48:25

@DavidHammen Ah ok, makes sense. The intuition behind the temperature of the space is failing me completely :)

#### @yo' 2015-01-30 15:49:04

@Svalorzen OTOH, the ball cools down on the touch, so I don't (didn't) see why the space should be that hot.

#### @Joe 2015-01-30 15:59:56

@yo' Those molecules that hit the earth (or whatever) do cool down "on the touch". However, the metaphor breaks down there: the sea transfers heat efficiently, while the universe is not dense, and so doesn't transfer heat efficiently.

#### @yo' 2015-01-30 16:04:10

@Joe yep I know. but the space does not (probably because the average temp of surfaces in space is 6kK?)

#### @Joe 2015-01-30 16:07:38

Space does not transfer heat efficiently because heat transfer (of gasses/plasmas) is related to the density of the medium. For heat to transfer atoms have to interact. When you have one atom per CC volume, that doesn't happen particularly often.

#### @rubenvb 2015-01-30 16:18:31

I've always found temperature to lose its usefulness when it comes to either near-vacuum or super-reactive plasma's like the quark-gluon plasma. I just think to much in terms of the pressure a gas exerts or the frequency spectrum a solid emits as temperatue I guess.

#### @Svalorzen 2015-01-30 16:36:01

@yo' I think you should stop considering space as a whole object/"thing". Try instead to consider it as literal space containing incredibly sparse, incredibly small, incredibly hot "things" (atoms).

#### @Maxter 2018-11-19 18:22:19

The answer should add that there is a cutoff frequency in space. The speed of sound is zero for most frequencies.

#### @iantresman 2015-01-29 09:56:32

You need to consider that space is filled with a tenuous plasma, which behaves slightly differently to an ideal gas. First, the electrons will carry sound at a different rate to the heavier protons, but also, the electrons and protons are coupled via the electric field. See: Speed (of sound) in plasma

The speed of sound in the solar wind is estimated at around 58 km/s, based on the equation in the answer given by Kieran Hunt. However, the temperature of the solar wind is more like $T = 1.2 \times 10^5K$ (ref)

#### @user56903 2015-01-29 09:03:21

Given the low density of gas, the speed of sound would be a direct function of the temperature of the gas ie the speed of the molecules/atoms. Since this varies from about 2.7K to millions of degrees near some stars, the speed of sound can change quite a bit.

### [SOLVED] Is the speed of sound observable without tools?

• 2016-03-10 09:10:17
• Zaibis
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• Tags:   acoustics