# Sound waves in carbon dioxide -- I think book answer is *wrong*

## Homework Statement

Sound waves can be refracted when they travel through balloons filled with different gases. How would the motion of a sound wave be changed if it traveled through a balloon filled with carbon dioxide?

BOOK ANSWER
"Being more dense than air, the carbon dioxide in the balloon will slow down the sound wave. This will tend to focus the sound together, like a lens. (A balloon filled with hydrogen do the opposite)"

INTERNET INFORMATION
"Sound waves refract in the same way as light waves. When a sound wave is slowed down it bends towards the normal line and when it speeds up it bends away from the normal line.
There is one big difference. Light waves slow down when they enter liquids and solids. Sound waves speed up in liquids and solids.
Sound travels well in solids because the particles are close together so vibrations can be easily passed along".

MY ANSWER
Sound waves in air will travel faster in denser liquids and solids (and gases????).
Sound travels well in denser materials because the particles are close together so the longitudinal vibrations can be easily passed along. So when sound waves (in air) enter the denser carbon dioxide filled balloon they will bend away from the normal line and travel faster (with larger wavelengths).

I think the book answer is wrong based on the internet information that I have read. Please advise.

## Answers and Replies

gneill
Mentor
Carbon dioxide gas is more dense than air (at the same temperature and pressure) because the individual particles are on average more massive, not because they are closer together. They move more slowly for a given kinetic energy (again, on average).

For gasses this is correct. For liquids and solid materials we can think that energy transportation through the mesh use other freedom degrees than kinetic, like harmonic oscillators. Combined oscillators on solids can transfer energy much more faster than free particle movements.

Carbon dioxide gas is more dense than air (at the same temperature and pressure) because the individual particles are on average more massive, not because they are closer together.
That's good info for me

v = √(γ R T / M) (https://en.wikipedia.org/wiki/Speed_of_sound#Details)
The bigger the molecular mass ( in this case CO2 ), the slower the sound travels in that medium
Thanks. You've got an equation and I can't argue with a equation so accept what you say.

So is it the case that sound waves travel more slowly in dense gases and faster in less dense gases BUT travel faster in solids than they do in gases even though solids are more dense than gases?

What about liquids? Do sound waves travel more slowly in dense liquids and faster in less dense liquids BUT travel faster in solids than they do in liquids even though solids are more dense than gases?

Models for solid are more complex. Let a line of harmonic oscillators combined each other. For the ##i\,th## oscillator you can make the wave equation by 2nd Newton's Law as something like this: $$\frac{d^2}{dt^2}x_i + c^2\,\frac{d^2}{dx^2}x_i = 0$$ where
## c = \omega_0\,d ## (##d## the distance between oscillators and ##\omega_0## the characteristic oscillator frequency).
You can take approximation values for ##\omega_0## for iron e.g. by melting and evaporation temperature. You can see that calculation gives you ##c>2.500(m/s)##.

gneill
Mentor
Sound will usually travel faster in solids than in gases or liquids because there are more ways to transfer energy between atoms or molecules that share bonds. But there are all sorts of bond structures, from long chain polymers to crystal lattices. Neutral gases pretty much have to move energy by travel and collision. I'm pretty sure that a solid could be designed to purposely conduct sound slowly.

Liquids can be more complicated because there are different kinds of loose bonds that can form between the molecules comprising a liquid. Take water for example, which is a polar molecule. There are electric dipoles at play.

Do a google search on "velocity of sound in various liquids". You should be able to find tables with plenty of examples to compare.

Models for solid are more complex. Let a line of harmonic oscillators combined each other. For the ##i\,th## oscillator you can make the wave equation by 2nd Newton's Law as something like this: $$\frac{d^2}{dt^2}x_i + c^2\,\frac{d^2}{dx^2}x_i = 0$$ where
## c = \omega_0\,d ## (##d## the distance between oscillators and ##\omega_0## the characteristic oscillator frequency).
You can take approximation values for ##\omega_0## for iron e.g. by melting and evaporation temperature. You can see that calculation gives you ##c>2.500(m/s)##.

I should have explained I'm High School level physics .... my fault.

The speed of sound is the square root of the elastic modulus divided by the density. For ideal gases, the bulk modulus is the pressure (but to be precise for sound one needs to take into account adiabaticity, this gets you terrid's equation). Liquids and solids are denser, but their bulk modulus is larger by a larger factor. It is on the order of 100 GPa. That is why sound in solids and liquids is faster.

That is why sound in solids and liquids is faster.

But is sound through solids faster than through liquids?

Sound travels faster through solids than liquids ???
Sound travels faster through liquids than gases
Sound through solids > liquids > gases ?????

But is sound through solids faster than through liquids?

Sound travels faster through solids than liquids ???
Sound travels faster through liquids than gases
Sound through solids > liquids > gases ?????
The big difference is with gases, so write ">>" there.
For solids it depend on shape, whether it is a longitudinal wave in a rod or in the bulk. Those two are different, with a similar difference with respect to sound in a liquid.

Hello I need to refresh this question please. Hence the use of color Make it as exciting as a new thread.

We decided that the speed of sound through solids > liquids >> gases and I looked through the table in the link .....
There are plenty of tables of data online.
http://www.rfcafe.com/references/general/velocity-sound-media.htm

There are exceptions to the statement that speed of sound through solids > liquids >> gases and one notable one is hydrogen. It travels in sound much faster than the other gases listed. Is it because of its small size. Helium is also a small molecule and sound travels through helium quickly too.

Oh .... just seen this .......

v = √(γ R T / M) (https://en.wikipedia.org/wiki/Speed_of_sound#Details)
The bigger the molecular mass ( in this case CO2 ), the slower the sound travels in that medium

So should I more accurately say sound travels through hydrogen faster than the other gases listed because it is of the smallest molecular size?

THE QUESTION WAS:
Sound waves can be refracted when they travel through balloons filled with different gases. How would the motion of a sound wave be changed if it traveled through a balloon filled with carbon dioxide?

Thanks for all the help. here is my final answer to the question:

Carbon dioxide gas is denser than air (at the same temperature and pressure) because the individual particles are more massive (than the molecules that form air), not because the molecules are closer together. Carbon dioxide molecules move more slowly than the other air molecules (on average) because of their larger molecular mass.
For gases the bigger the molecular mass (in this case CO2) the slower the sound travels in that medium. When the sound waves from air enter the balloon they will slow down and diffract towards the normal.

haruspex
Science Advisor
Homework Helper
Gold Member
So should I more accurately say sound travels through hydrogen faster than the other gases listed because it is of the smallest molecular size?
Not size, mass.
The mechanisms by which sound travels in gases, liquids and solids are different. That is the primary cause of the speed differences. For a given mechanism, the more massive the molecule the slower the speed.
Your final answer in post #15 is fine.

Not size, mass.
The mechanisms by which sound travels in gases, liquids and solids are different. That is the primary cause of the speed differences. For a given mechanism, the more massive the molecule the slower the speed.

Hello. By massive do you mean large in mass?

I've been thinking of massive in general English language use to mean large size (as in length, width, diameter). I was not thinking of mass.

So I should change my final answer in #15 to:
Carbon dioxide gas is denser than air (at the same temperature and pressure) because the individual molecules of CO2 have a greater mass (than the molecules that form air), not because the molecules are closer together. Carbon dioxide molecules move more slowly than the other air molecules (on average) because of their larger molecular mass.
For gases the bigger the molecular mass (in this case CO2) the slower the sound travels in that medium. When the sound waves from air enter the balloon they will slow down and diffract towards the normal.

haruspex
Science Advisor
Homework Helper
Gold Member
Hello. By massive do you mean large in mass?

I've been thinking of massive in general English language use to mean large size (as in length, width, diameter). I was not thinking of mass.

So I should change my final answer in #15 to:
Carbon dioxide gas is denser than air (at the same temperature and pressure) because the individual molecules of CO2 have a greater mass (than the molecules that form air), not because the molecules are closer together. Carbon dioxide molecules move more slowly than the other air molecules (on average) because of their larger molecular mass.
For gases the bigger the molecular mass (in this case CO2) the slower the sound travels in that medium. When the sound waves from air enter the balloon they will slow down and diffract towards the normal.
More massive means greater in mass, so your answer in post #15 is equivalent to your answer in post #17. Both are fine.
Perhaps in post #15 you was right by accident, i.e. you meant something other than what you wrote, but what you wrote was correct.

Perhaps in post #15 you was right by accident, i.e. you meant something other than what you wrote

You're right. Thanks for all your help

While I'm here .... and just before this thread loses energy ... I want to ask about the speed of sound in diamond:
http://hyperphysics.phy-astr.gsu.edu/hbase/tables/soundv.html

I saw a question about speed of sound in diamond a while ago. Speed of sound in diamond is very fast compared to say metals. Why would this be? I read somewhere about sound needing SHEAR FORCES (or maybe that was for mechanical transverse waves). Anyway diamond is such a rigid structure that how could it possibly transfer vibrations causing sound when it is so rigid?

Last edited:
haruspex
Science Advisor
Homework Helper
Gold Member
I saw a question about speed of sound in diamond a while ago. Speed of sound in diamond is very fast compared to say metals. Why would this be? I read somewhere about sound needing SHEAR FORCES (or maybe that was for mechanical transverse waves). Anyway diamond is such a rigid structure that how could it possibly transfer vibrations causing sound when it is so rigid?
The more rigid, the higher the speed of sound, no?

The more rigid, the higher the speed of sound, no?

Si

Okay got it. I just thought that the solid structures needed to have a little give. Not so much give as liquids but just to move a little.

haruspex
Science Advisor
Homework Helper
Gold Member
Ci

Okay got it. I just thought that the solid structures needed to have a little give. Not so much give as liquids but just to move a little.
No structure is completely rigid.

No structure is completely rigid

Yes got it. Diamond is completely rigid so sound passes though at high speed

haruspex
Science Advisor
Homework Helper
Gold Member
Yes got it. Diamond is completely rigid so sound passes though at high speed
Nothing is completely rigid. If completely rigid the speed would be infinite.

Nothing is completely rigid. If completely rigid the speed would be infinite.

One inaccurate use of a word seems to change everything in physics.