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The speed of sound on Mars

Waves, sound and light · level 4, lesson 2 of 6

A question to start

On Earth, sound travels at about 340 m/s. On Mars it is about 240 m/s, nearly a third slower. Is it slower because the air is thin?

The idea

Surprisingly, no. The speed of sound in a gas hardly depends on its pressure or density. It depends on two other things:

  • Temperature: in warmer gas, the particles move faster and pass the push along faster.
  • Mass of the particles: heavy particles are slower to get moving.

A rough rule is that the speed goes with \(\sqrt{T/M}\), where \(T\) is the temperature in kelvin and \(M\) the mass of the particles (their molar mass).

Speed of sound Mars Earth
Main gas carbon dioxide nitrogen and oxygen
Average particle mass (molar mass) 43.5 g/mol 29.0 g/mol
Average temperature 214 K (−59 °C) 288 K (15 °C)
Speed of sound about 240 m/s about 340 m/s

So Mars air carries sound slowly because it is cold and made of heavy particles.

EarthMars240 m/s340 m/s

Worked examples

1. The rule for Earth. \(\sqrt{288/29.0} = \sqrt{9.93} = 3.15\).

2. For Mars. \(\sqrt{214/43.5} = \sqrt{4.92} = 2.22\).

3. The ratio. \(2.22/3.15 = 0.70\), and \(0.70 \times 340 = 238\) m/s, close to the measured 240 m/s.

Try it

  1. Does the thin air make sound slower on Mars?
  2. Give the two reasons sound is slower on Mars.
  3. On a summer afternoon on Mars, the air near the ground warms up. Does sound go faster or slower?
  4. Use the rule to find how much faster sound goes in Earth air at 308 K than at 288 K.
Answers
  1. No. The speed hardly depends on pressure or density.
  2. Mars air is colder, and its particles are heavier.
  3. Faster.
  4. \(\sqrt{308/288} = 1.034\): about 3% faster.

Common mistake

"Thin air, slow sound." Thin air makes sound quieter, not slower. Mars's sound is slow because the air is cold carbon dioxide.

Where it leads