# Why exactly do higher frequency (>240 Hz) sounds on Mars travel ~4% faster than lower frequencies? What's the physics and are there optical analogies?

SciTech Daily's April 1, 2022 Variable Speed of Sound on Mars: What Sounds Captured by NASA’s Perseverance Rover Reveal About the Red Planet says

The result of the recordings: a new understanding of strange characteristics of the Martian atmosphere, where the speed of sound is slower than on Earth – and varies with pitch (or frequency). On Earth, sounds typically travel at 767 mph (343 meters per second). But on Mars, low-pitched sounds travel at about 537 mph (240 meters per second), while higher-pitched sounds move at 559 mph (250 meters per second).

The variable sound speeds on the Red Planet are an effect of the thin, cold, carbon dioxide atmosphere. Prior to the mission, scientists expected Mars’ atmosphere would influence sound speed, but the phenomenon had never been observed until these recordings were made. Another effect of this thin atmosphere: Sounds carry only a short distance, and higher-pitched tones carry hardly at all. On Earth, sound might drop off after about 213 feet (65 meters); on Mars, it falters at just 26 feet (8 meters), with high-pitched sounds being lost completely at that distance.

and links to the April 1, 2022 paper in Nature In situ recording of Mars soundscape

Abstract:

Prior to the Perseverance rover landing, the acoustic environment of Mars was unknown. Models predicted that: (i) atmospheric turbulence changes at centimeter scales or smaller at the point where molecular viscosity converts kinetic energy into heat1, (ii) the speed of sound varies at the surface with frequency2,3, and (iii) high frequency waves are strongly attenuated with distance in CO22–4. However, theoretical models were uncertain because of a lack of experimental data at low pressure, and the difficulty to characterize turbulence or attenuation in a closed environment. Here using Perseverance microphone recordings, we present the first characterization of Mars’ acoustic environment and pressure fluctuations in the audible range and beyond, from 20 Hz to 50 kHz. We find that atmospheric sounds extend measurements of pressure variations down to 1,000 times smaller scales than ever observed before, revealing a dissipative regime extending over 5 orders of magnitude in energy. Using point sources of sound (Ingenuity rotorcraft, laser-induced sparks), we highlight two distinct values for the speed of sound that are ~10 m/s apart below and above 240 Hz, a unique characteristic of low-pressure CO2-dominated atmosphere. We also provide the acoustic attenuation with distance above 2 kHz, allowing us to elucidate the large contribution of the CO2 vibrational relaxation in the audible range. These results establish a ground truth for modelling of acoustic processes, which is critical for studies in atmospheres like Mars and Venus ones.

Question: Why exactly do higher frequency (>240 Hz) sounds on Mars travel ~4% faster than lower frequencies? What's the physics and are there optical analogies?

Yes sound is generally a scalar wave under normal conditions and for optics/EM we usually use vector waves, so I've asked only for possible analogies rather than a 1:1 correspondence.

The discussion in Nature is likely to have the basis of an answer, but it's pretty in-depth and thorough and I'm hoping there's a way to explain the physics in simpler terms and draw an analogy to some optical dispersion phenomenon I might be more familiar with.

Potentially related sound on Mars questions in Space SE:

Whenever a parcel of atmosphere undergoes some physical change the thermodynamic equilibrium is changed. For example, suppose that a sound wave is propagating and leads to a compression, reducing the local volume. This compression leads to a new equilibrium state for the translational, rotational, and vibrational energies of the atmosphere, and there is a finite time scale associated with the redistribution of the energy. These time scales can vary from the order of $$10^{-10}$$ seconds for translational energies to $$10^{-3}$$ seconds for nitrogen vibration. I am not sure what the relaxation time for the vibrational states of carbon dioxide is (especially at low pressures), but I would assume it would be no lower than the nitrogen vibration time.