Velocity of sound in Carbon Diox vs. Air

In summary: Consider that air is mostly N2.For a given amount of kinetic energy (temperature), how does the velocity of a nitrogen molecule compare to that of a carbon dioxide molecule?Nitrogen has more kinetic energy than CO2, so it will have a higher velocity.
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Homework Statement



An organ pipe is blown with carbon dioxide and produces waves 2 ft long and a note with a frequency if 350 Hz. What is the velocity of sound in carbon dioxide? How do you account for the fact that this is not the same as the velocity in air?


Homework Equations



Wavelenght=velocity/frequency therefore Velocity=wavelength*frequency.

The Attempt at a Solution


Velocity =2ft*350HZ=213.36 m/s

My teacher wants the answer in the same units as the question, but 700 ft/Hz doesn't seem like a true meausrement? Which is why I put 213.36 m/s? I am on track here?

Also, would this velocity be different than that of air b/c carbon dioxide is heavier and denser than air?
 
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  • #2
Yes and that is because v = sqrt( krt/m0) where k stands for adiabatic exponent.
 
  • #3
kriegera said:

Homework Statement



An organ pipe is blown with carbon dioxide and produces waves 2 ft long and a note with a frequency if 350 Hz. What is the velocity of sound in carbon dioxide? How do you account for the fact that this is not the same as the velocity in air?


Homework Equations



Wavelenght=velocity/frequency therefore Velocity=wavelength*frequency.

The Attempt at a Solution


Velocity =2ft*350HZ=213.36 m/s

My teacher wants the answer in the same units as the question, but 700 ft/Hz doesn't seem like a true meausrement? Which is why I put 213.36 m/s? I am on track here?
What's wrong with ft/s?
Also, would this velocity be different than that of air b/c carbon dioxide is heavier and denser than air?
That's one reason. What else does the speed of sound in a gas depend on, and is it or are they different for CO2 compared to air?
 
  • #4
vela said:
What's wrong with ft/s?

That's one reason. What else does the speed of sound in a gas depend on, and is it or are they different for CO2 compared to air?

How would you convert: 213.36 m/s into ft/s?

Thanks for the tip!
The speed of a gas also depends on its temperature. (Velocity increases with temperature. Temperature also affects density the higher the temp, the lower the density.) Therefore, the velocity of carbon dioxide would differ from air b/c of differences in temperatures based on the kinetic energy of molecules in the air and CO2.
 
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[To convert 213.23 m/s to ft/s we would get: (213.36 m/s)( 3.2808399)= 700 ft/s]

Correct?
 
  • #6
kriegera said:
[To convert 213.23 m/s to ft/s we would get: (213.36 m/s)( 3.2808399)= 700 ft/s]

Correct?

Yes you really didn't need to do that since 2*350 = 700
 
  • #7
AtticusFinch said:
Yes you really didn't need to do that since 2*350 = 700

So i can leave it in m/s? Where did the 350 come from?
 
  • #8
kriegera said:
So i can leave it in m/s? Where did the 350 come from?

You should know you calculated it yourself in your first post.

Velocity =2ft*350HZ = 700 ft/s

Hz is defined as s-1 "per second"
 
  • #9
AtticusFinch said:
You should know you calculated it yourself in your first post.

Velocity =2ft*350HZ = 700 ft/s

Hz is defined as s-1 "per second"

gosh-sometimes you miss the obvious staring at you. thanks!
 
  • #10
kriegera said:
Therefore, the velocity of carbon dioxide would differ from air b/c of differences in temperatures based on the kinetic energy of molecules in the air and CO2.

Assume the carbon dioxide is the same temperature as air, because you're not told otherwise.

Consider that air is mostly N2.

For a given amount of kinetic energy (temperature), how does the velocity of a nitrogen molecule compare to that of a carbon dioxide molecule?
 

1. How does the velocity of sound in carbon dioxide compare to that in air?

The velocity of sound in carbon dioxide is significantly higher than in air. This is because carbon dioxide has a higher molecular weight and density compared to air, allowing sound waves to travel faster through the medium.

2. Does the temperature affect the velocity of sound in carbon dioxide?

Yes, the velocity of sound in carbon dioxide is affected by temperature. As temperature increases, the molecules in carbon dioxide move faster, resulting in an increase in the velocity of sound.

3. What is the speed of sound in carbon dioxide at room temperature?

The speed of sound in carbon dioxide at room temperature (around 25 degrees Celsius) is approximately 259 meters per second, which is about 1.6 times faster than in air at the same temperature.

4. How does the pressure of the medium affect the velocity of sound in carbon dioxide?

The pressure of the medium does not have a significant effect on the velocity of sound in carbon dioxide. This is because the speed of sound is primarily determined by the density and molecular weight of the medium, which are not significantly affected by pressure changes.

5. Does the composition of carbon dioxide affect its velocity of sound?

Yes, the composition of carbon dioxide can affect its velocity of sound. For example, if the carbon dioxide is mixed with other gases, such as oxygen or nitrogen, the velocity of sound may be slightly different due to the different molecular weights and densities of these gases.

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