Gases and sound waves

Factual Questions
1

Here is what I have so far, correct me if I’m wrong. Assume I am just speaking regularly and this is what happens to my voice.
Lighter gases will increase the frequency
Density will not affect the frequency
Lighter density will attenuate the volume meaning at the same distance with a thinner density my voice will have less volume.

Are there any other effects that gases have on a speaking voice?
Are their formulas for these effects so for example if my voice is 40dB @ 100 yards I could calculate the dB if it were 8 psi. Or if I have a 1200Hz sine wave in our air it would be X Hz in pure carbon dioxide.

2

Are you confusing the helium effect on the vocal cords with other acoustic effects?

The medium that sound travels through will affect the speed of propagation and the efficiency (sustaining the amplitude of the wave, i.e. loudness)

And, now that I think about it, perhaps the density of the medium will affect different frequencies differently (as you implied in a way). Certainly, as you dunk your head in a swimming pool, the timbre of sound is greatly changed, implying that certain frequencies are being attenuated.

3

No I am not. I’m using the fact that the speed of sound is higher in a lighter medium. Would that not raise the frequency all else being equal?

4

I think you are confusing terms.

Lighter gases are density. Where you say “density”, you are talking about pressure.

I’m not able to answer the questions about how precisely the changes affect the sound.

5

This depends somewhat on what you mean by ‘frequency’.

Your vocal cords are going to vibrate at the same frequency. That doesn’t change.

But the timbre can be affected. Think helium - your vocal cords (or a guitar string, if you prefer some other source) produce sound at the same frequency no matter what because they vibrate the way they vibrate but the timbre is affected because the speed of sound in helium is different than in regular air so how the sound resonates in your throat, your mouth, and in the air itself will change.

6

Speed of sound varies about 10:1 depending on the gas. Hydrogen at 1300 m/s, Helium 973 m/s, Air 331 m/s down to the favourite SulfurHexaflouride at 133 m/s.

But as we will see, density important.
Hydrogen 0.09g/l Helium 0.166g/l Air 1.3g/l SulfurHexaflouride 6.16g/l Perfluorobutane 11.2g/l

Speed of sound might have a slight direct effect, but isn’t the dominant effect on the vocal tract. We mostly don’t contain sound waves bouncing off things. We contain Helmholtz resonators, and these are defined by the compressibility of the gas and the mass of gas present, so the volumetric density of gas.
The speed of sound is in principle defined by the compressibility and volumetric density V = \sqrt{K/\rho} so it appears in discussions - but it is confusing as it isn’t representing the propagation speed of sound. It appears because it depends on the same underlying parameters that define the Helmholtz resonances.

A well known Helmholtz resonator is to blow over the neck of a bottle. It makes a tone. The frequency is, perhaps counter intuitively, not defined by the height of the bottle. It is a function of the volume of the bottle, the height of the neck and the diameter of the neck. And the gas. The gas in the main volume of the bottle is simply providing a spring (so compressibility), and the mass of air in the neck is providing a mass that resonates with the spring (so density). Take a second bottle with a neck half the height, but the same volume and the resonant frequency is much higher. (A simple open hole operates as a neck due to end effects. A round hole appears as a neck 1.7 times the hole diameter. The same end correction needs to be added to any actual neck as well.) Flute and Ocarina are other Helmholtz resonator examples.

Similarly, our vocal tract is highly dependant upon the diameter and length of components and thus the mass of air in those components, and the volume of gas in those components. These define the frequencies they tend to select. Whistling - the frequency depends the size of the lips opening and the volume of air in the mouth behind.

The volume of air in the pharynx acts as a spring against the mass of air in the passages leading to it, but will act as a mass. So it gets complicated. Similarly, the volume of the mouth and the effective cross sectional area.
As we speak or sing we modify the cross sectional area of these passages, and this modification changes the mass of air in them, which changes the resonances present. The very harmonic rich output from the vocal cords is passed through what is effectively a dynamically modified band pass filter, which provides the final sound.

The nasal volume is also there acting as a spring, but we can’t modify its volume on demand. Get a bad cold, and the nasal passages close up, leading to a change in diameter of passages, which leads to increased frequency of resonance and the characteristic nasal sound. Holding one’s nose has the same effect - the closing of the nose removes an effective moving mass (the air in the nose proper) from the resonant system, thus increasing the resonant frequency.

TL;DR:
Gas properties affect the voice. But it isn’t the speed of sound directly that is the determinant. It is the volumetric density of the gas and the compressibility of the gas.
The speed of sound may appear in Helmholtz frequency calculations, but that is an artefact, as it just turns out to be a convenient unit to combine density and compressibility.

Breathing Sulfur-Hexaflouride and Perfluorobutane will do exactly what one might hope for.

7

Let’s leave out the effect on the larnyx for a second and assume a speaker. That may or may not make a difference, I don’t know but I’m more interested on the effect of the soundwaves themselves although I do recognize that the characteristics of the gas may effect the speaker’s production of sound waves.

So I have a 1200Hz tone at 14.7 psi in Earth’s atmosphere 80% N2 20% O2 that is 40dB at 100 yd. What would I hear if I play that same tone on a speaker in CO2 at 7 psi @ 100 yards? What effect does each variable have? Are there other variables that would affect the tone?

8

If the speaker diaphragm is vibrating with a pure tone of 1200 Hz in the carbon dioxide, then the air molecules would still vibrate at that same frequency, and so would your eardrum, and so would the ciliae in your inner ear. So you would hear the same pitch as in a normal atmosphere.

The speed of sound does change in a different atmosphere, but that would just affect how long the signal takes to get to you and the wavelength of the sound waves that travel to your ear.

9

Gasses are not perfect media for sound waves. They are slightly dispersive, and slightly non-linear. Over 100 yards air adsorbs higher frequencies more than low, something that is humidity dependant as well. There will likely be a difference with CO2, but hard to quantify.

Transmission also has the curious effect of sharpening the waveform. This becomes apparent the further the wave propagates. The compression side of the wave travels ever so slightly faster than the rarefaction - because it is travelling in slightly more compressed gas - so the waveform becomes slightly distorted over distance. This effect is the same for any gas. Basically because sound propagation is adiabatic rather than isothermal. The exact magnitude of the effect is probably gas dependent in horrible ways.

The biggest difference you will get with a conventional cone loudspeaker and different gasses will be from simple impedance matching. At half atmospheric pressure the sound energy coupled from the loudspeaker will be significantly lower.

Carbon Dioxide has a STP density of about 2g/l and speed of sound of 260m/s. Its impedance will be a bit different to air at the same pressure, but the mooted pressure difference will dominate effects without worrying about the actual gas.

A loudspeaker will also behave differently in lots of other ways. 1200Hz is something of a difficult frequency range for most loudspeakers. The conventional direct radiator (ie cone loudspeaker) doesn’t perform well here as the wavelength is getting too small and the radiation pattern becomes tighter and develops lobes. Loudspeaker designs are usually crossing over between low frequency drivers and high frequency drivers at this point. As the speed of sound drops in the new atmosphere directivity changes and the radiation pattern will change.

If we were to consider loudspeakers designed for outdoor use at scale we would be using slightly horn loaded drivers at 1200Hz. They would still be affected by impedance matching and directivity issues. The change in gas density would likely wreck the basic parameters of their design in other ways as well. Loudspeaker cavities, either for bass enclosures, or the phase plug and horns for horn loaded drivers depend on the gas properties. So the loudspeakers would be expected to not operate as designed, with expected resonances shifting significantly, and horn operation (a black art at best) going weird. Minimally no longer exhibiting a flat frequency response. Horns have all sorts of evil distortion mechanisms and a lot of care is needed to ameliorate them. So even a pure tone may become noticeably distorted when a horn is operating outside of its design regime.

So a single tone radiated from a loudspeaker would almost certainly drop in amplitude a significant amount in 7 psi CO2, although the exact amount would be the result of a lot of interrelated effects.
Music playing in such a system would sound bad. Not because of the sound propagation, but because the loudspeaker would not be able to operate properly.