Relationship between displacement, velocity, and acceleration - diyAudio
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Old 19th February 2013, 01:26 AM   #1
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Default 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.
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Old 19th February 2013, 03:31 AM   #2
gootee is offline gootee  United States
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I assume that you already know how it works for moving objects, in physics/mechanical dynamics: a = dv/dt = dx/dt, 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.
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Old 19th February 2013, 05:51 PM   #3
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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?
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Old 19th February 2013, 08:17 PM   #4
sreten is offline sreten  United Kingdom
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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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Old 19th February 2013, 08:24 PM   #5
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Quote:
Originally Posted by sreten View Post
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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Old 19th February 2013, 09:26 PM   #6
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Quote:
Originally Posted by weltersys View Post
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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Old 20th February 2013, 02:05 AM   #7
gootee is offline gootee  United States
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Quote:
Originally Posted by Jabbejokker View Post
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.
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Old 20th February 2013, 04:01 PM   #8
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Quote:
Originally Posted by sreten View Post
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.
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Old 21st February 2013, 05:02 AM   #9
gootee is offline gootee  United States
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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.
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Old 22nd February 2013, 01:47 PM   #10
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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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