Woofer speed

...and its meaning and influences...


I got to one article about woofer speed written by some wannabe professional from Adire Audio (as it is stated in the document). The document can be found here:
Link to the article

Briefly, author took the well known Newton law
where F is the force, m represents mass and a is for acceleration.
Force in loudspeakers can be represented as the product F=Bl.I where Bl is force factor (related to voice coil length l (voice coil height is something different, this is simply the length of the wire in magnetic gap) and magnetic induction B) and I stands for the current).

So we get
Bl.I = m.a

and for acceleration
a = Bl.I/m

This is all simple physics, in our country 11-year old children already know this. But the author then replaces time invariant constants Bl and m by C, which is absolutely wrong. You can't replace them both by the same constant when they are not equal!

Here is the proof
If you got two speakers with the same Bl, and the same current through the coil I, but one of them (speaker 1) has got Mms = 100g and the other (speaker 2) has got Mms = 200g you get

a1 = a2
Bl.I/m1 = Bl.I/m2

and because Bl.I is the same on both sides
1/m1 = 1/m2
and finally
m1 = m2

so, as the author tells in his scientific article
100g = 200g
and that is simply a revolution in math.

Theoretical part of the article is simply an absurdity.

Now to the measurement. Author thinks that doubling the moving mass should have the same effect as doubling the inductance. But that is not true. If we look at the equivalent scheme of the speaker

We can clearly see that the only element in the electric part (elektrická časť) that has an effect on the impulse response is the inductance. But in the mechanical part (mechanická časť) we do also have Cms - suspension compliance, which reduces the overall impact of Mms change on the impulse response.

In the measurement itself, 28.5 gram mass is added to the cone of the relatively small 6,5" woofer with original Mms of 24.39 gram. If author is right, adding even a battle tank on the cone would have no effect on the impulse response. So why didn't he add more weight? 150g for example? Was he afraid?

And when looking at the graph, author only looks at the first peak, but what about the rest of the signal? You can clearly see that with the mass added the blue line (impulse response of the speaker with added mass) doesn't copy the red one (original) as accurately as the green one (added inductance) does.