Speed Of Sound On A Humid Day

Classical Mechanics Level 1

How does the speed of sound change on a humid day, as compared to a dry day at the same temperature?

Decreases Stays the same First decreases then increases Increases

1 solution

Upamanyu Mukharji
Feb 10, 2016

Speed of sound in air is determined by the following relation: $V=\sqrt{\dfrac Ed}$

Where $E$ denotes the elasticity of medium, and $d$ denotes the density of medium.

thus $V$ is inversely proportional to square root of density.

When it is humid, the air is less dense, thus as compared to a hot day speed of sound is greater!

Moderator note:

Good explanation.

The key to this question is to understand how the density of air changes.

To what extent can the difference in speed of sound be noticed?

Yes , you are correct , density of humid air is less than dry air. Weird...

Nihar Mahajan - 5 years, 4 months ago

No problem..... It's a weird fact of life....

Upamanyu Mukharji - 5 years, 4 months ago

Just think about it.

Water vapor, which is $\ce{H2O}$ , is much lighter than $\ce{N2}$ and $\ce{O2}$ , which form most of air on Earth. Hence, water vapor is less dense than dry air.

Thus, humid air, which is a mix of dry air and water vapor, will be less dense than dry air and denser than water vapor.

Calvin Lin Staff - 5 years, 3 months ago

Speed Of Sound On A Humid Day

1 solution

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