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CharlieM 19th August 2021 12:22 PM

Diaphragm damping effect of surrounding air
I read somewhere that a low mass ESL diaphragm very effectively damped by a higher mass of air surrounding it and coupling to it.

I’ve been pondering the damping effect of the surrounding air mass, and how to quantify it. The problem is that I lack physics smarts and I really suck at math.

If the damping volume is merely equivalent to the diaphragm’s excursion x area, then the answer is air density x that volume.

But my gut feel is that the actual damping volume must be greater than merely the equivalent volume of the diaphragm’s excursion, because that volume of air would not be pushing into a surrounding space that’s empty and devoid of air, but into a surrounding sea of air. And if so; the coupling would not cease sharply at the diaphragm’s excursion limit but would progressively decrease with increasing distance from the diaphragm.

If the above is correct; I’m thinking that a quantifying equation must factor in the compressibility of the air at room temp & sea level pressure.
And I figure the air eventually gets out of the way of the progressing displacement and de-couples from the diaphragm, but I have no clue how to quantify the effective damping volume/mass of that air, or even determine whether the damping volume equates to only the equivalent diaphragm excursion or extends beyond it.

Would anyone care to share their thoughts on this?

golfnut 19th August 2021 09:11 PM

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Hi CharlieM

You are close to correct with your guess. There are two distinct parts to the effect you describe.

First, when the membrane moves, it compresses the air causing an acoustic wave to spread out from the points where compression occurs - this is what we hear as sound. The air movement is in the same direction as the movement of the membrane and energy is radiated away from the speaker.

Secondly, there is a kind of sloshing (a technical term :D) of the air around the membrane - much the same as the sloshing effect around a spoon when you stir your coffee. In this case, there is no compression of the air (so no sound), no energy loss.

The first effect corresponds to the radiation resistance of the ESL. It is the dominant part of the radiation impedance at high frequencies. The radiation resistance is constant at high frequencies, but falls away very quickly at low frequencies (depends on the area of the membrane)

The second effect corresponds to the imaginary part of the radiation impedance (analogous to inductance) and gives the membrane its apparent mass - think about the airmass trapped in a bedsheet when it's shaken. This effect happens at the lowest frequencies only and dies off at higher frequencies, so it has a constant air mass at low frequencies but it gets less as the frequency increases.

The combination of the two means that at high frequencies, the Q of the system (Q= Mass/Resistance, analogous to L/R is an electrical system) is very small (grossly over damped), while at very low frequencies, it is underdamped - hence the membrane resonance and need for additional damping.

See attached Figure - Vertical axis is impedance, horizontal axis is frequency (scaled by size of speaker).

Green curve is imaginary part of the impedance - rises in proportion to f at low frequencies = constant mass in this region.

Red curve is the resistance, which rises as f^3 at low frequencies and is constant at high frequencies.

ESLs mostly operate in the region where the resistance is constant. The curves for conventional loudspeakers are similar, but they operate at low frequencies where the radiation resistance is negligible.

CharlieM 20th August 2021 12:48 AM

OK... bookmarking this one!

Thanks, my friend.

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