Question

Sound waves are longitudinal waves that can travel through air. Would you expect sound waves to travel faster through a low-density gas (such as helium) or a higher-density gas such as carbon dioxide? Justify your answer based on what you have learned.

Answer 1

Answer:

Sound waves travel faster in a low-density gas

Explanation:

First of all, let's remind that sound waves are pressure waves: they consist of oscillations of the particles in a medium, which oscillate back and forth along the direction of motion of the wave (longitudinal wave).

The speed of sound in an ideal gas is given by the equation

$v=\sqrt{\gamma \frac{p}{\rho}}$

where

$\gamma$ is the adiabatic index of the gas

p is the gas pressure

$\rho$ is the gas density

From the equation, we see that the speed of sound is inversely proportional to the square root of the density: therefore, the lower the density, the faster the sound waves.

So, sound waves will travel faster in a low-density gas.