Which way is up? (Which way does a loudspeaker driver move?)

[Tim Link]

If we animate pressure, velocity, acceleration, and displacement, we this:
View attachment 292706
Displacement, velocity, and acceleration all peak at the same places in SPACE for this standing wave situation, but not at the same TIME. Mixing up what is coming from the signal and what is coming from the wave is something I see all the time.

Thanks for putting this together! I got lost with this though. I don't see any three things peaking at the same point in space. It looks like they're peaking at the same time but at different points in space. The x-axis is distance, right? Only the light blue and green lines seem to peak at the same points in space, and they're 180 degrees out of phase.

 

[René - Acculution.com]

Thanks for putting this together! I got lost with this though. I don't see any three things peaking at the same point in space. It looks like they're peaking at the same time but at different points in space. The x-axis is distance, right? Only the light blue and green lines seem to peak at the same points in space, and they're 180 degrees out of phase.

The red clearly peaks at the same place as those two. This is to illustrate than one needs be careful when jumping to the conclusion that a quarter period in space corresponds with 90 degree phase shift. It is not that simple.

 

[sonitus mirus]

The red clearly peaks at the same place as those two. This is to illustrate than one needs be careful when jumping to the conclusion that a quarter period in space corresponds with 90 degree phase shift. It is not that simple.

There is nothing simple about any of this, though I do appreciate your contribution, and I am working to understand it.

 

[Tim Link]

The red clearly peaks at the same place as those two. This is to illustrate than one needs be careful when jumping to the conclusion that a quarter period in space corresponds with 90 degree phase shift. It is not that simple.

Yup, it clearly does. I don't know why it didn't look that way to me at first.

 

[René - Acculution.com]

Yup, it clearly does. I don't know why it didn't look that way to me at first.

Good . I get confused myself looking at this. It is better do the math and trust that instead of looking at plots only.

 

[Cbdb2]

In a recent video by PS Audio/Paul, he mentions the sentiment that many probably share with him, that a loudspeaker driver works by compressing air as it moves outwards. This illustrates perfectly that you can work with loudspeakers for decades without ever understanding how a loudspeaker actually works. As we will see in a minute, there is rarefaction as the driver moves outwards, and compression as it moves inwards.

Let us first discuss why intuition tells us to agree with Paul. It could be that you think about sticking your hand out the car window and feeling the pressure pushing back on your hand, and so there effectively is 'positive' or forwards displacement with your hand to the air molecules resulting in a positive pressure. Or you might think about the driver moving outwards for a positive DC voltage from a battery, and that is what is tripping you up. Or maybe you are thinking about the pressure in an enclosure, not necessarily a loudspeaker but a bike pump, where you push the piston in a 'positive' direction and get a positive pressure. But we are talking about acoustics with wave propagation here, and not fluid flow. And how a driver behaves at DC is not how it behave above its characteristic frequency. And free field is different than an enclosure.

If we look at the pressure generated in free field from a flat piston in a baffle, we can calculate analytically calculate the pressure generated via the so-called First Rayleigh integral [Fourier Acoustics, E.G. Williams].
View attachment 269995
The pivotal point here is the sign on the righthand side. With w(Q) being the outwards displacement in a point Q on the piston, it is clearly seen that for a piston radiating into free space (mass-like impedance), this displacement is in anti-phase with p(P); the pressure in a measurement point P. This is really all we need to see. There, in general, is a 180 degree phase difference between the outwards displacement of a loudspeaker and the resulting pressure. Which of course means that when it moves outwards, defined as a positive displacement, we clearly get a negative pressure!

Well this paper does not have the -sign in the integral.

https://www.acoustics.asn.au/conference_proceedings/INTERNOISE2014/papers/p898.pdf

How does a pressure sensitive mic in a kick drum show a positive transient?

https://gearspace.com/board/low-end-theory/418822-kick-drum-waveform-example-should-look-like.html

 

[jackocleebrown]

Well this paper does not have the -sign in the integral.

https://www.acoustics.asn.au/conference_proceedings/INTERNOISE2014/papers/p898.pdf

How does a pressure sensitive mic in a kick drum show a positive transient?

https://gearspace.com/board/low-end-theory/418822-kick-drum-waveform-example-should-look-like.html

You mean in this equation?

This equation is in terms of velocity, not displacement. Velocity is the rate of change of displacement, so you can relate the "w" in Rene's equation to the "vp" in this equation like this:

Put this into the equation from the paper and you have

j is the imaginary operator, so

Hey presto, once it's written in terms of displacement you have the -sign back again:

The main takeaway from René's post is that the radiated sound pressure is proportional to the cone acceleration, not the cone displacement.

 

[BeerBear]

The math and physics here is beyond my knowledge and I'm looking for a dumbed down explanation.
I'm mostly wondering whether OP's finding contradicts what's written in some technical literature about microphones and speakers. For example in this PDF:

An audio signal is deemed to be positive when it results from in an increase in the acoustic pressure on the microphone diaphragm, and thus in the displacement of the diaphragm towards the rear.

a terminal of a transducer has positive polarity when (...) an instantaneous positive voltage at that terminal produces an outward movement of the diaphragm

 

[Cbdb2]

I assume OT meant this video

Paul seems like a nice guy, and a lot of people praise him for "easy to understanding explanation", some even call him genius...
If I didn't know better, I'd trust him too

Easy to understand, often wrong explanations.

 

[Cbdb2]

You mean in this equation?
View attachment 314790
This equation is in terms of velocity, not displacement. Velocity is the rate of change of displacement, so you can relate the "w" in Rene's equation to the "vp" in this equation like this:
View attachment 314801
Put this into the equation from the paper and you have
View attachment 314802

j is the imaginary operator, so
View attachment 314806

Hey presto, once it's written in terms of displacement you have the -sign back again:

View attachment 314807

The main takeaway from René's post is that the radiated sound pressure is proportional to the cone acceleration, not the cone displacement.

Thanks. He was talking about cone movement and then gave an equation for cone displacement and now your talking about acceleration, a little confusing. Whats the equation for pressure from cone acceleration?
From the cone displacement equation don't you get the same pressure (positive) at one (positive) displacement regardless of cone direction? And the cone displacement changes from negative to positive during its forward movement, does that mean the pressure reverses at zero displacement while its moving forward?

 

[Hayabusa]

The math and physics here is beyond my knowledge and I'm looking for a dumbed down explanation.
I'm mostly wondering whether OP's finding contradicts what's written in some technical literature about microphones and speakers. For example in this PDF:

Indeed this is how it is!
At DC (when speaker and room are perfectly sealed) and very low frequencies it is like that.

 

[audiofooled]

Thanks. He was talking about cone movement and then gave an equation for cone displacement and now your talking about acceleration, a little confusing. Whats the equation for pressure from cone acceleration?
From the cone displacement equation don't you get the same pressure (positive) at one (positive) displacement regardless of cone direction? And the cone displacement changes from negative to positive during its forward movement, does that mean the pressure reverses at zero displacement while its moving forward?

Direction may be the confusing part. Perhaps this can help:

Phase Relationships for Plane Waves

 

[BeerBear]

Indeed this is how it is!
At DC (when speaker and room are perfectly sealed) and very low frequencies it is like that.

I don't mean the part about how polarity is defined, but how in most literature: positive voltage = forward movement of the speaker cone = positive pressure change. (A microphone recording is the same, but with the membrane going in the opposite direction.)

This is from an AES paper:

In a similar manner, when a positive polarity is applied to a loudspeaker, it may move forward and cause a compression at its surface, while a negative polarity causes the loudspeaker to move backward whereupon it generates a rarefaction in the air.

Isn't this in contradiction with what's stated in the OP?

The reason I ask is because EBU and AES seem reputable sources. So either I'm missing something or, according to OP, they're wrong.

 

[Cbdb2]

Direction may be the confusing part. Perhaps this can help:

Phase Relationships for Plane Waves

If Im standing facing north so the direction of the wave is left to right pressure and velocity are in phase. If I turn around to face south and the wave is now going right to left there out of phase?
If you take a velocity sensitive mic and a pressure sensitive mic they would be in phase in one direction and out of phase if turned 180 degrees?

 

[Cbdb2]

A condenser mic is a pressure sensor. Push the capsules front you get a positive voltage. A kick drum without its resonant head is a flat piston. A mic in a kick drum shows positive pressure from forward movement.

https://gearspace.com/board/low-end-theory/418822-kick-drum-waveform-example-should-look-like.html

 

[dasdoing]

How ported speakers (excited Helmholtz Resonators) really work, with regard to the port action.

 

[neRok]

Or as we show below, the pressure will be zero, when the displacement is zero:

I thought I was following along, but this graphic doesn't seem to match the description?




Is the animation from the start of this video correct? (source)

 

[neRok]

Maybe this isn't the best thread to discuss this, but I've been reading a lot of threads on phase and keep seeing KSTR prove that polarity flip can be audible in bass tones. So it seems like getting the woofers output to match the source phase is important so that the "absolute phase" is correct in the bass region. But when you consider all the different speakers with different crossovers (passive or not), who knows how they actually behave when wired up + to +? And even if the speaker is "correct", what if the DAC caused a flip a in the signal chain for example? So I wonder, is there are a reliable method to check this? Because its been suggested in this thread that some microphones can be polarity flipped too? So I wonder if anyone has verified the UMIK-1's polarity when recorded by REW for example? Or maybe there is a simple hands-on test that can be performed to confirm the absolute phase?

 

[audiofooled]

If Im standing facing north so the direction of the wave is left to right pressure and velocity are in phase. If I turn around to face south and the wave is now going right to left there out of phase?

No. The wave won't change it's direction because of the way you are facing it. If you were to observe the same particle, it will either be pushed by the positive pressure or pulled by the negative pressure, depending on wave direction.

If the wave is traveling from left to right, then the observed particle would be pushed from left to right by the positive pressure, because the particles to the left of it are in the state of compression, and ones to the right of it are still in the state of equilibrium. So, pressure and particle velocity are in phase.

If the wave is traveling from right to left, the observed particle will be pulled by the negative pressure, again from left to right, because the particles to the right of it are in rarefaction, and particles to the left of it are still in equilibrium state. In this case, pressure and particle velocity are out of phase.

 

[René - Acculution.com]

I don't mean the part about how polarity is defined, but how in most literature: positive voltage = forward movement of the speaker cone = positive pressure change. (A microphone recording is the same, but with the membrane going in the opposite direction.)

This is from an AES paper:

Isn't this in contradiction with what's stated in the OP?

The reason I ask is because EBU and AES seem reputable sources. So either I'm missing something or, according to OP, they're wrong.

The say that "the cone may move forward for a positive voltage" without really going into the nitty-gritty. This will of course depending on how they wire it up, but in general it will move outwards for a positive voltage BELOW its characteristic frequency, but inwards then for the frequencies where the music is playing. So it all fits together. Haven't read it detail, but if you see something strange it, please outline it, and I will have a look ;-)