# Relationship between displacement, velocity, and acceleration

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#### Jabbejokker

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.

#### gootee

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.

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#### 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?

#### 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.

#### weltersys

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. .

#### john k...

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.

#### gootee

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.

#### Jabbejokker

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.

#### gootee

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.

#### Jabbejokker

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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