Velocity of sound coooool but how?

[perfectz]

Friends,
I am clear of the fact that, the velocity of sound depends on temperature, and am absolutely not disagreeing...

I browsed and understood the concepts of positive temperature gradient and negative temperature gradient, and thereby the concepts of sound speed gradient(positive and negative).

BUT HOW IN THE GOD DAMNED HELL...
How do they say that the velocity of sound is directly proportional to the temperature?

please help me out...

 

[ice109]

where does it say this? because i don't think it is true.

 

[perfectz]

surf wikipedia

 

[Ryle]

Sound is the transmission of vibrational waves through the medium of air. Temperature is defined as a measurement of the overall average kinetic energy of molecules of a system. So then if these waves are transmitted by the bouncing of air molecules against each other, then the rate of transmission must depend upon the inherent properties of how fast these air molecules are normally bouncing around and hitting each other.

 

[FredGarvin]

What is the problem with the statement that sound speed is proportional to the temperature of the medium it is traveling in? Are you having issues with the phrase "directly proportional?"

 

[Dick]

surf wikipedia

Wikipedia says that it is proportional to the square root of the temperature for ideal gases. Which expression seems to be saying 'directly proportional'?

 

[perfectz]

ok then
the velocity of sound at a higher temperature is is more when compared with the velocity of sound at a lower temperature.
Why?
What decreases the velocity of sound at lower temperature?
Is it because of the lack of energy in the molecules of cold air, that they cannot transmit the work done by sound on them, more faster?
Or is it the density of air playing the vital role in the reduction of sound velocity, as height increases?
What is it? pleaseeeeeeeeeeeeeeeeeeeeeeee.....

 

[Dick]

If you peruse the wiki thing a little more thoroughly, they state the velocity is proportional to sqrt(pressure/density). Just like in a wire with pressure playing the role of a tension. Keeping only nonvarying factors for a given molarity of ideal gas pressure is proportional to T/V whereas density is proportional to 1/V.

 

[andrevdh]

Sound is transmitted through a medium by forcing the molecules/particles in it to vibrate to and fro. The actual amplitudes of vibration is quite small (I seem to recall something in the order of a tenth of a millimeter [for air at STP]). These vibrations are transmitted via collisions between the particles (electrostatic repelling forces acting during the collisions). The speed of propagation of the vibrations therefore depends on how fast the disturbance can be transmitted between neighbouring molecules. In denser media this delay time between transmissions will be reduced. Also if the molecules are moving faster the collisions will be transmitted at a higher speed than when the molecules move slower.

 

[perfectz]

Ok then...
Lets assume that I am in Berlin and you are in London.
Let's assume that the air densities are the same, both at Berlin and London.
Let the temperature at Berlin be 20 degree Celsius.
Let the temperature at London be 15 degree Celsius.
Now if you use the formula to calculate the velocity of sound,(velocity of sound in gas formula), you'll see that sound travels more faster in Berlin than London.
I DON'T SEE DENSITY PLAYING A ROLE IN HERE...

Is temperature, density, pressure related to each other?
I know that, as temperature increases, pressure increases.What role does density have to play in the velocity of sound?

 

[andrevdh]

The average speed of warmer air is higher than that of colder air. This means that the delay time between transferrence of disturbances in warmer air will effectively be shorter (distances is covered faster between molecules).

There is no fixed relation between temperature, pressure and volume for the atmosphere since it is not confined per se. But one can apply the laws roughly if considering a volume of air of "reasonable" size during transitions. This is precisely the reason why weather prediction is not an exact science, but a sort of guessing game.

 

[perfectz]

so can we come to a conclusion density and pressure has no role in determining the velocity of sound?
If yes Please explain......

 

[FredGarvin]

So now you are questioning the relationship to density? First you were questioning the proportionality to temperature.

In your example, you constrain both places to have the same densities and different temperatures. Therefore, the pressures have to be different. Then you can say

$$c = \sqrt{\gamma R T}$$

With basic thermo equations of state this is equivalent (in a perfect gas) to

$$c = \sqrt{\frac{\gamma P}{\rho}}$$

If you look at a table of the standard atmosphere values, as altitude increases, temperature decreases as does density and so does the speed of sound. However, once about 65,000 ft is reached, you hit a temperature inversion where the density and thus pressure still decrease, but temperature increases. At that point the speed of sound starts to increase again up to 200,000 ft.

 

[perfectz]

BANG ON TARGET......
Thats what I needed.....
At 65,000ft to 200,000ft, Temperature increases due to the absorption of U-V rays by the ozone.
OR DOES IT?

 

[DaveC426913]

Is temperature, density, pressure related to each other?
I know that, as temperature increases, pressure increases.

Pressure increases only with a fixed volume. If volume is free to change, then a temperature increase causes a volume increase, thus a density decrease.

 

[FredGarvin]

At 65,000ft to 200,000ft, Temperature increases due to the absorption of U-V rays by the ozone.
OR DOES IT?

That is the reason I have always been given.

http://en.wikipedia.org/wiki/Stratosphere