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.

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

[tex]v=\sqrt{\gamma \frac{p}{\rho}}[/tex]

where

[tex]\gamma[/tex] is the adiabatic index of the gas

p is the gas pressure

[tex]\rho[/tex] 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.

ajeigbeibraheem ajeigbeibraheem · Answer 2 · 2021-11-29T13:23:16+01:00

We would expect sound waves to travel faster through a low-density gas of helium than a higher-density gas like carbon dioxide.

In a medium, the speed of sound can be expressed by using the relation;

[tex]\mathbf{v = \sqrt{\gamma \Big(\dfrac{p}{\rho}}\Big)}[/tex]

here;

speed = v
the medium adiabatic index = γ
the pressure = p
the density = ρ

It is obvious that the speed of the sound through the medium varies inversely proportional to the square root of the gas density.

As such, it implies that the lower the density, the faster at which the speed waves will travel.

Therefore, we can conclude that we would expect sound waves to travel faster through a low-density gas of helium than a higher-density gas like carbon dioxide.

Learn more about sound waves here:

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