[timbley]

Is the pressure in front of the speaker cone highest when the cone is moving fastest, or when it is at its furthest excursion point? Or somewhere in-between?

I've been pondering this ever since reading this article about doppler distortion by Rod Elliot:
http://sound.whsites.net/doppler.htm

He asserts ( if I read correctly ) that the pressure is greatest when the cone is at its furthest excursion point. This seems odd to me because the cone is not moving at that point. Sound pressure is moving away at the speed of sound, and the cone never moves anywhere near fast enough to keep up.

I did some web searching but couldn't find a definitive answer. Any help would be greatly appreciated!

[JohnR]

Neither - SPL is proportional to cone acceleration. Without knowing specifically which part of the article you are referring to, I suspect you have misinterpreted what Eliot has said.



Interesting topic though, I must have another look.

[timbley]

Acceleration would be maximum at the peaks of excursion. Is that right? It's doing a full 180 course change at that point.

I'm looking at this animation of a pendulum showing acceleration force maxing out at the max excursion points:
https://physics.stackexchange.com/questions/233193/direction-of-velocity-and-acceleration-for-a-pendulum

If it's true that max SPL happens when the cone is at max acceleration then that would imply the pressure is greatest when the cone velocity is zero and it is at its maximum acceleration back in the other direction. How can that be? It seems intuitive to me that pressure will be greatest in front of a diaphragm when it's moving the fastest.

[timbley]

Here's part of Rod's article that's giving me pause, specifically the part I colored red:

"If the shift is a genuine Doppler shift, then we will see the signal compressed or stretched at the zero crossing points of the LF waveform, and at the peaks of the LF waveform the HF signal should be in phase, since LF cone movement is effectively zero (for a moment in time, at least). "

Interestingly, his measurements seem to suggest that he is correct in this assertion. I just can't understand how it could be true. Could it be that there's a phase shift between those frequencies from his speaker and it's throwing off the measurement? Or maybe the recording room volume is small enough and the bass frequency low enough that the pressure really is highest at peak excursion? At 50Hz the wavelength is 22.5 feet, so if he did this in a really small lab it might be that the whole room was evenly pressurizing from the cone movement, which would make his assertion correct.

[Tyson]

The cone doesn't have to be moving at the speed of sound in order to induce a doppler effect.  Remember, the doppler effect was first noticed with the sound of sirens on ambulances.  Ambulances certainly don't move at the speed of sound.

[timbley]

I agree!

What I was trying to say is that the air pressure moves away at the speed of sound unless it is contained,  so to get max pressure at max excursion you'd have to get the cone there impossibly fast.


The question is: When is the air pressure in front of the cone the highest? When it's moving fastest, or when it's at it's peak of excursion?  It seems to me that it's when the cone is moving fastest, unless the air is contained in a small enough volume. In that case pressure will be greatest at peak excursion. I think I've heard this called the oil can effect.

[JohnR]

The question is: When is the air pressure in front of the cone the highest? When it's moving fastest, or when it's at it's peak of excursion?

Neither - it's when the acceleration is greatest. If the signal is a sine wave then the peak excursion does also happen to be the maximum acceleration. (With the sign reversed.)

[timbley]

Thanks John R for answering my question. How did you learn this about maximum acceleration of the cone being the point of maximum pressure? I can't seem to find that information anywhere. Anything you could recommend that I read?

[Doublej]

Thanks John R for answering my question. How did you learn this about maximum acceleration of the cone being the point of maximum pressure? I can't seem to find that information anywhere. Anything you could recommend that I read?

Possibly explained here:

https://www.klippel.de/fileadmin/_migrated/content_uploads/Klippel__Schlechter__Distributed_parameter.pdf

[JohnR]

Thanks John R for answering my question. How did you learn this about maximum acceleration of the cone being the point of maximum pressure? I can't seem to find that information anywhere. Anything you could recommend that I read?

Hi, this is just the physics: velocity is the derivative of distance (displacement), acceleration is the derivative of velocity. If displacement is a sine function, velocity is cosine, and acceleration is -sine.

Actually the pendulum animation you posted before illustrates it.

[Update] Here is a graph:


From https://www.spaceagecontrol.com/calcsinm.htm

[timbley]

Thanks Doublej and JohnR. That Klippel paper is very interesting. I think I'll be looking at that for a while!

Yes, the pendulum diagram I showed indeed shows what you've been saying, that acceleration of the cone is greatest at the peaks of excursion.
What I'm thinking is that there's a confusion here. We need to consider the acceleration of the air molecules in front of the cone instead of the cone's own acceleration. When do the air molecules reach their peak acceleration? That's when we get peak pressure. I think it's at the zero crossing point of the driver, when it's acceleration is at a minimum and its speed at max, ramming into the air and squishing it.

I'm trying to think up an experiment to make sure I'm wrong about this.

[ClefChef]

Neither - it's when the acceleration is greatest. If the signal is a sine wave then the peak excursion does also happen to be the maximum acceleration. (With the sign reversed.)

Peak acceleration in the sine wave of the cone movement is at the x zero. At peak excursion acceleration is the lowest.

[JohnR]

Peak acceleration in the sine wave of the cone movement is at the x zero. At peak excursion acceleration is the lowest.

You are writing "acceleration" when you should be writing "velocity". Please refer to the graph I posted above.

I'm trying to think up an experiment to make sure I'm wrong about this.

Not sure what kind of experiment you had in mind, but suppose you played a tone at some frequency and SPL and measure the excursion. Then play a tone at half the frequency and same SPL and measure the excursion. If SPL is proportional to velocity then the excursion will be double. If SPL is proportional to acceleration then excursion will be 4x.

[Elizabeth]

THe peak air pressure would be somewhere before maximum excursion forward, of the cone.
I am certain there is some complex math which could show the air pressure in front of the cone!
As a thought experiment alone, The air cannot move out of the way as fast as the cone is moving forward from the start at the lowest cone position. As the cone accelerates forward the air pressure is building up from a negative to mean air pressure.. past the average in the room probably a little before the cone reaches the midpoint (at least some..) and still building as the cone is moving forward..
As the cone reaches nears the end of the excursion the wave in front of it reaches a maximum, and is already decreasing in pressure at the piston surface as the piston reaches the max forward point (since the velocity of the piston is dropping rapidly).

[timbley]

Not sure what kind of experiment you had in mind, but suppose you played a tone at some frequency and SPL and measure the excursion. Then play a tone at half the frequency and same SPL and measure the excursion. If SPL is proportional to velocity then the excursion will be double. If SPL is proportional to acceleration then excursion will be 4x.

Measured total SPL is directly proportional to acceleration of the cone. I totally agree with that, but that's not what I'm asking.

I'm asking when during the cone's excursion is pressure greatest in front of the cone. I would need to do something like put a pressure meter on the speaker cone and film it in slow motion playing a 20hz tone.
One simple example might be to put a bubble wand on the end of a long heavy pendulum and get it swinging. At what point in the pendulum's swing do you think the most bubbles will get made? It takes pressure across the wand to blow bubbles. I'm pretty sure it's going to happen when the pendulum crosses through its zero crossing point, where it's moving fastest, not at the peaks of it's excursion. It's experiencing max acceleration out there, but it's not moving through the air so it can't be transferring energy to accelerate the air and create pressure.

[timbley]

THe peak air pressure would be somewhere before maximum excursion forward, of the cone.
I am certain there is some complex math which could show the air pressure in front of the cone!
As a thought experiment alone, The air cannot move out of the way as fast as the cone is moving forward from the start at the lowest cone position. As the cone accelerates forward the air pressure is building up from a negative to mean air pressure.. past the average in the room probably a little before the cone reaches the midpoint (at least some..) and still building as the cone is moving forward..
As the cone reaches nears the end of the excursion the wave in front of it reaches a maximum, and is already decreasing in pressure at the piston surface as the piston reaches the max forward point (since the velocity of the piston is dropping rapidly).

This all makes sense to me. The exact point of max pressure may change with the relationship of the max speed of the cone compared to the speed of sound, and maybe some other factors, such as the presence of a horn and compression chamber. But it can't be at the end of the piston's max forward point, when it has momentarily ceased all motion.

[JohnR]

It's experiencing max acceleration out there, but it's not moving through the air so it can't be transferring energy to accelerate the air and create pressure.

You're saying that despite the fact that the cone is at its maximum acceleration, the air is not accelerating at all.

[DaveC113]

It might be easiest to look at it in terms of the cone has finished doing all the work on the air once it's at it's max excursion. At that instant it's not doing any more work on the air, yet at the same time the air has been compressed or refracted to it's maximum.

When the cone is at it's highest velocity it's right in the middle of doing work on the air, and still has 50% left to go.

[JohnR]

Hm...

[Doublej]

This might help inform or confuse the topic:

https://www.har-bal.com/wp-content/uploads/Speaker_theory.pdf