Particle displacement vs time graph of sound. How can this happen?

[sameeralord]

Hello everyone ,

I'm so confused with particle displacement vs time graph and pressure vs time graph of sound. I thought maximum displacement of a particle is its compression and minimum displacement is its rarefaction. For some strange reason the graphs show exactly the opposite. How can the particles be at atmospheric pressure when the displacement is maximum. Your help would be greatly appreciated. Thanks

 

[Doc Al]

You need to understand how to read the displacement graph. If there were no sound wave, there would be undisturbed particles at every point x. The displacement at coordinate x tells you the displacement of the particles whose undisturbed position is at x. Thus if the displacement is a maximum at point x, it means that the particles that usually reside at point x have been displaced to the right (positive direction); If the displacement is a minimum, it means they've been displaced to the left. Thus the position where the pressure is maximum would be between a maximum and minimum of displacement. Make sense?

 

[jtbell]

Note that in an ideal gas, pressure is proportional to density, when the temperature is kept constant.

Looking at your displacement graph, the molecules that are normally at x = 0 have moved to the right (+x direction), and the molecules that are normally at x = 18 have moved to the left. So in the region between x = 0 and x = 18, the density of the gas is higher than normal, and so is the pressure.

 

[sameeralord]

Thanks both of you for your replies They were both very helpful!

That was a great response jtbell I think I got it. Is it when particles move right and then particle further move left high pressure region is caused meaning compression and vise versa for rarefaction.

However as I just realized this is a displacement distance of wave graph. However my graph in my notes is identical but it has time in the axis. This is the closest pic I found in the interent. It is basically the same graph but with time in the x axis. I don't think it would make a difference. Would it? If that is so I got it

Thanks again for your replies!

 

[Razi Rehman]

This information is really very helpful ... thanks :D

 

[FranciscoAlm]

Hello there!
I understood in part what you have said here. But how can compression and rarefaction regions correpond to zero particle displacement?

 

[FranciscoAlm]

Nevermind, I got it :)
Thank you anyway!

 

[AlephZero]

Look at this animation. It's easiest to see if you see the option to "both ends of the tube closed".
http://www.physics.smu.edu/~olness/www/05fall1320/applet/pipe-waves.html