Relationship of excursion, surface and low frequency produced?

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Hello,
I would like to know what is the relationship between Excursion Xmax, Surface area Sd, of the driver and the Frequency it can Produce?
(I am trying to compare passive radiator in terms of this quality)
Thanks in advance.
 
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Generally Hoffman iron law stands as follows....Pick 2 of three characteristics

1 small enclosure
2 deep bass reproduction
3 high efficiency

This 8s the case in subwoofers in which the electric motor operates close to stall ( low excursion).
 
As to piston size vs frequency output drops at square of inverse hz below resonance.

This is due to the diagram not being able to 'grip' the air and it moving slower to reproduce longer wavelengths.

The solution is a diaphragm which in creases surface area as frequency drops, TRW-17 or propeller on a plane as used for braking.
 
2XmaxSd = volume displaced. More volume displacement means louder bass. Has nothing to do with what frequency it could produce.

For passive radiator you need to know how heavy is the cone and how much weight you could bolt on to lower...to tune your pr.
 
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