The speed of light in a vacuum is the same wherever you measure it in the universe, according to Einstein's special theory of relativity. Whether you're sat on Earth, Mars, or Zoozve, if you measure the speed of light you'll find it chugging along at a cool 299,792,458 meters per second (983,571,056.43 feet per second), the absolute speed limit of the universe.
Sound is not the same as light. As the poster for Alien explains, in space no-one can hear you scream. Or to put it another way which won't sell as many movie tickets, sound cannot travel through a vacuum because it is a vibration propagating as an acoustic wave through a medium, be it liquid, solid, or gas.
Sound moves at different speeds through those mediums, traveling faster at through greater densities. On Earth, sound moves at 1,500 meters (5,000 feet) per second in water, and in air around 340 meters (1,115 feet) per second. In solids, sound moves much faster, though how fast depends on the solid. Scientists attempting to calculate the fastest that sound could possibly travel found that it decreases with the mass of the atom, implying that sound would be fastest if it were to propagate through solid hydrogen. Though solid hydrogen only occurs at astonishingly high pressures like those found inside gas giants like Jupiter, they calculated that sound would move along at 36 kilometers per second (22 miles per second) in it, likely the fastest possible speed that sound can travel.
This leads us to answer the question in the title of this article. Earth's atmosphere is much thicker than Mars', being roughly 100 times more dense on our planet's surface than on the red one. As such you'd expect sound to travel slower there than here, if the atmosphere is thick enough to carry sound any significant distance at all.
Of course, we have recordings of sound on Mars, including that of a Martian dust devil, thanks to the army of robots we have sent there. So we know that sound travels there experimentally.
In fact, Mars is one of only two planets where we have actually measured the speed of sound. In an experiment in 2022, NASA's Perseverance rover fired lasers at rocks and waited for the resulting shockwave to be heard by its microphones. Just like on Earth, the speed of sound varies depending on temperature and altitude, but experiments conducted by the rover found that the speed of sound in the Jezero Crater averaged out to around 240 meters per second (540 miles per hour).
As day changes to night on Mars, the speed was found to vary by around 10 percent, because of the resulting drop in temperature. Sound on Mars doesn't stop being weird there though. Due to how sound travels through carbon dioxide at low pressure, Mars goes through a change in the speed of sound in the audible bandwidth.
"For an acoustic wave with a frequency higher than ~240 Hz [just below middle C on a piano], CO2 vibrational modes activated through collisions do not have time to relax their energy," the team explained in their paper. "It turns out that, on Mars, frequencies above 240 Hz travel more than 10 m/s faster than low frequencies. It may induce a unique listening experience on Mars with an early arrival of high-pitched sounds compared to bass."
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