How does sound change high in atmosphere? [duplicate]

There is no sound in space because there are not enough particles to transmit the pressure wave. But what about really high in the atmosphere where there is just a little air? Would sound move faster, slower or at the same speed? Would the intensity (aka volume) go up, down, or stay the same? And would the frequency go up, down, or stay the same as it traveled through space?

• There is an earlier physics.stackexchange question that is very related, titled sound propagation at low pressure That question got some relevant comments, but no answer. There is a short document (google for it using its title: 'Transmission of Sound Waves in Gases at Low Pressures'. By the looks of it that document contains information that is of interest to you. That same google search may also give you other material, that reverences the above article. Commented Aug 11, 2019 at 14:53

Would sound move faster, slower or at the same speed?

In general, it would be slower. The speed of sounds is NOT dependent on pressure, but it increases with temperature. Since it gets colder the higher you go, the lower the speed of sound will be. At -70C it's about 285 m/s down from 343 m/s at room temperature.

It would be even slower on Mars since the predominant gas on Mars is Carbon Dioxide and not Nitrogen.

Would the intensity (aka volume) go up, down, or stay the same?

This depends a bit on how the sound is created in the first place, but for most sound sources it will go down. Most sources are volume velocity source, i.e. things wiggle and move X volume of gas per second. In the far field the resulting pressure is related by the field impedance of the medium: $$Z_m = \rho c$$, where $$\rho$$ is the density and $$c$$ is the speed of sound. The density drops with pressure and both density and speed of sound drop with temperature. The intensity is the product of pressure and particle velocity and will be significantly lower.

And would the frequency go up, down, or stay the same as it traveled through space?

Depends again on the sound source. If a loudspeaker cone wiggles 100 times per second, so will the air molecules and so will you ear drum. There would only change a change in frequency if the gas itself is part of the sound source (say an organ pipe or flute for example).

To add a few things to Hilmar's great answer, the speed of sound in an ideal gas (which is a good approximation at sea level and even better higher up where the atmosphere is thinner) is

$$c = \sqrt{\frac{\gamma k}{m} T},$$

where $$\gamma$$ is the adiabatic index (and $$\gamma \approx 1.4$$ for gases of two-atomic molecules), $$k = 1.380649 \times 10^{−23}\,\text{J/K}$$ is Boltzmann's constant, $$m$$ is the average molecular mass, and $$T$$ is the temperature in Kelvin. Thus, we can see that the speed of sound goes with the square root of temperature, given that the mix of gases is the same. As the temperature decreases higher in the atmosphere, so will the speed of sound.

As this equation depends on the equations of fluid mechanics, it holds as long as fluid mechanics holds. However, fluid mechanics assumes that a fluid is a continuum, i.e., a continuous blob of matter where we ignore the fact that it's made out of molecules. As the atmosphere gets thinner, the molecules are further apart, and the continuum assumption starts to break down.

How well the continuum assumption holds is described by the Knudsen number,

$$\mathrm{Kn} = \frac{L_\mathrm{mfp}}{L},$$

where the mean free path $$L_\mathrm{mfp}$$ is the average path that a molecule takes between collisions with other molecules, and $$L$$ is some length that depends on your problem. In our case, we are looking at sound propagation, and $$L$$ is typically a representative wavelength of our wave. This means that the above equation for the speed of sound no longer holds when the frequency is extremely high (so that the wavelength is extremely short) or the gas is extremely thin.

So, can sound still propagate in very thin gases such as the very upper layers of the atmosphere? The answer is yes. In the 50s and 60s, this was studied theoretically by people like Wang-Chang, Uhlenbeck, and Foch, and experimentally by people like Meyer, Sessler, and Greenspan. Even for extremely thin gases, where $$\mathrm{Kn} \gg 1$$, you can have sound propagation, although the sound attenuates very quickly with propagation distance, and the speed of sound changes with $$\mathrm{Kn}$$ in addition to the temperature. For $$\mathrm{Kn} \gg 1$$ (i.e., in extremely thin gases), measurements in noble gases shows that the speed of sound is around twice of that for $$\mathrm{Kn} \ll 1$$ at the same temperature.

The speed of sound at sea level on a very mild day is 767mph, but this varies slightly according to temperature and barometric pressure. The speed of sound is less in warm air or at altitude, because it depends on the density of the medium. At 50,000 feet it is only 659mph. For aircraft, the speed of sound is known as Mach 1, which will vary according to height and other factors. An aircraft flying at Mach 2 is flying at twice the speed of sound. The speed of sound is important to aircraft because the flying characteristics of an aircraft change at what used to be called "the sound barrier", ie about 767mph at sea level. In fact, drastic changes take place shortly before the speed of sound is reached, but modern supersonic aircraft are designed to cope with this. The intensity of the sound also varies with altitude. On Mars the air is very thin, about the same as at about 100,000 feet on Earth. You would have to wear a space helmet if you walked in the open on Mars, but I have often wondered whether it would be possible to hear anything if a radio or some other sound generator, like a geologists hammer for instance. were in use not very far away.

(This is not an answer, it's just that it's too large for a comment)

As it happens a couple of days ago Derek Muller (youtube science education channel: Veritasium) released a video about the upcoming Mars Helicopter.

The lift is provided by two counterrotating rotors, 1.2 diameter.

The rotors of the Mars Helicopter turn at 2500 rpm

Testing is done in a vacuum chamber that is many meters across, so they can replicate the density and composition of the Mars atmosphere.

In the video you hear quite a loud sound when the helicopter is in flight. (Link to the relevant part in the video: the sound of the Mars Helicopter)

(However, it's not clear to me whether that is sound picked up by a microphone located inside the vacuum chamber, or that the sound is loud even outside the vacuum chamber.)