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Sound in thin air

Waves, sound and light · level 4, lesson 1 of 6

A question to start

Scientists studying Perseverance's recordings worked out that the same sound source would sound about 20 dB quieter on Mars than on Earth. Why would thin air make sounds quieter?

The idea

A vibrating surface, like a loudspeaker cone, makes sound by pushing on the air next to it. How much sound energy it sends out depends on how hard the air pushes back. Thick air pushes back hard and takes in a lot of energy. Thin air pushes back weakly, and takes in little.

A good measure of how hard air pushes back is its density times its speed of sound:

\[\text{push-back} = \text{density} \times \text{speed of sound}.\]
Push-back of the air Mars Earth
Density 0.016 kg/m³ 1.217 kg/m³
Speed of sound about 240 m/s about 340 m/s
Density × speed about 3.8 about 414

Earth's air pushes back about 110 times harder. So the same speaker sends about 110 times less sound energy into Mars air. That is about 20 dB less, just what the scientists found.

Earth: strong soundMars: about 20 dB quieter

Worked examples

1. The ratio. \(414 \div 3.8 \approx 110\).

2. In decibels. 10 dB is 10 times; 20 dB is \(10 \times 10 = 100\) times. 110 times is just over 20 dB.

3. Far away. A sound that is 60 dB at 1 m on Earth would be about 40 dB at 1 m on Mars: like a quiet library instead of a conversation.

Try it

  1. Why does a speaker send less sound energy into thin air?
  2. How many times harder does Earth's air push back than Mars's?
  3. How many times less energy is a sound that is 20 dB quieter?
  4. A machine makes 80 dB of sound on Earth. About how loud would it be on Mars, at the same distance?
Answers
  1. Thin air pushes back weakly, so it takes in less energy.
  2. About 110 times.
  3. 100 times less.
  4. About 60 dB.

Common mistake

"Sound on Mars is quiet because it is far away." It is quieter even close by, because the thin air takes in so little energy from whatever is vibrating.

Where it leads