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Two speeds of sound

Waves, sound and light · level 4, lesson 3 of 6

A question to start

Perseverance timed two kinds of sound on Mars: the low hum of the Ingenuity helicopter and the sharp crack of its own laser hitting rocks. They did not travel at the same speed. How can that be?

The idea

On Earth, all sounds travel at the same speed. On Mars, the scientists found two speeds, about 10 m/s apart:

Speed of sound Mars Earth
Below about 240 Hz (low notes) about 240 m/s about 340 m/s
Above about 240 Hz (high notes) about 250 m/s about 340 m/s

The reason lies in how carbon dioxide particles store energy. Each one can spin and wobble as well as move. When a sound squashes the gas, some of the energy goes into these wobbles. But in thin air, particles bump into each other rarely, so the wobbles are slow to take up energy. For a fast vibration (a high note), they cannot keep up, and the gas behaves a little "stiffer", so the sound goes a little faster.

starthigh note: 250 m/slow note: 240 m/sthe high note gets there first

Worked examples

1. 100 m away. Low note: \(100/240 = 0.417\) s. High note: \(100/250 = 0.400\) s. The high note arrives 0.017 s sooner.

2. 1 km away. Low: 4.17 s. High: 4.00 s. Now the gap is 0.17 s, enough to hear.

3. On Earth. There is no gap: high and low notes arrive together.

Try it

  1. How far apart are Mars's two speeds of sound?
  2. Which arrives first on Mars, a high note or a low note?
  3. Find the gap in arrival times for a sound from 500 m away.
  4. Why do Mars's carbon dioxide particles react differently to high and low notes?
Answers
  1. About 10 m/s.
  2. The high note.
  3. \(500/240 - 500/250 = 2.083 - 2.000 = 0.083\) s.
  4. In thin air they collide rarely, so their spins and wobbles cannot keep up with fast vibrations.

Common mistake

"High notes always travel faster." On Earth, at everyday pressures, all notes travel at the same speed. The split is something special about thin carbon dioxide air.

Where it leads