Relationship between displacement, velocity, and acceleration - diyAudio
 Relationship between displacement, velocity, and acceleration
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 19th February 2013, 01:26 AM #1 diyAudio Member   Join Date: May 2010 Relationship between displacement, velocity, and acceleration I'm trying to figure out how the relationship of the above parameters play out in a transmission line or any other speaker. What leads what and how does it affect sound. Thank you.
 19th February 2013, 03:31 AM #2 diyAudio Member   Join Date: Nov 2006 Location: Indiana Blog Entries: 1 I assume that you already know how it works for moving objects, in physics/mechanical dynamics: a = dv/dt = d²x/dt², or x(t) = displacement or distance at time t v(t) = dx/dt a(t) = dv/dt So also, x(t) = ∫ v(t) dt + v(0) v(t) = ∫ a(t) dt + a(0) where the integrals are from 0 to t. I too would be interested to know if or how anything like that applies, in transmission line speakers. Last edited by gootee; 19th February 2013 at 03:41 AM.
 19th February 2013, 05:51 PM #3 diyAudio Member   Join Date: May 2010 Well, I am reading Martin Kings white paper on TL anatomy and I am getting stuck trying to understand how displacement precedes, acceleration which precedes acceleration. I am trying to visualize it in my head. How is displacement able to precede acceleration phase wise?
 19th February 2013, 08:17 PM #4 diyAudio Member RIP   Join Date: Nov 2003 Location: Brighton UK Hi, They don't precede each other, they are instantaneously 90 degrees out phase with each other as they have to be. Velocity is maximum at zero displacement and zero at maximum displacement. Acceleration is opposite to the displacement so the driver moves back and forth. rgds, sreten.
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Quote:
 Originally Posted by sreten Hi, They don't precede each other, they are instantaneously 90 degrees out phase with each other as they have to be. Velocity is maximum at zero displacement and zero at maximum displacement. Acceleration is opposite to the displacement so the driver moves back and forth. rgds, sreten.
And with enough magnetic force, electrical and acoustic damping, it moves back and forth in a close approximation of the amplified signal source. .

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Quote:
 Originally Posted by weltersys And with enough magnetic force, electrical and acoustic damping, it moves back and forth in a close approximation of the amplified signal source. .
Depends on what frequency you are talking about.
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Quote:
 Originally Posted by Jabbejokker Well, I am reading Martin Kings white paper on TL anatomy and I am getting stuck trying to understand how displacement precedes, acceleration which precedes acceleration. I am trying to visualize it in my head. How is displacement able to precede acceleration phase wise?
Just draw a sine waveform and call it displacement.

Then below that draw the SLOPE of the displacement plot. That's velocity.

Below that, draw the slope of the velocity plot. That's acceleration.

It's more interesting with something other than a sine wave.

diyAudio Member

Join Date: May 2010
Quote:
 Originally Posted by sreten Hi, They don't precede each other, they are instantaneously 90 degrees out phase with each other as they have to be. Velocity is maximum at zero displacement and zero at maximum displacement. Acceleration is opposite to the displacement so the driver moves back and forth. rgds, sreten.
Its difficult for me to understand how Velocity of air is at a maximum at zero displacement. To me if something (air) is accelerated it is displaced. How can something be at maximum acceleration and be at zero displacement ergo stationary?

Thanks for responding.

 21st February 2013, 05:02 AM #9 diyAudio Member   Join Date: Nov 2006 Location: Indiana Blog Entries: 1 A speaker cone gets pushed away from zero (don't count the zero displacement at the beginning, maybe). It gets close to its maximum displacement and slows down amd stops then moves back toward the center (zero displacement) position. It flies through the center position and goes to the other extreme, where it stops and reverses direction again. Its velocity is at maximum when it passes back through the zero-displacement position, each time.
 22nd February 2013, 01:47 PM #10 diyAudio Member   Join Date: May 2010 That makes sense. Displacement in reference to datum position. I guess thats where I got hung up. Thanks a lot everyone!

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