Question about spl, Qts, wattage etc

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I am trying to understand a few things about how these are interrelated - or not related.

Higher the Qts the stiffer the cone and foam is right ?

That means it takes more wattage to move it a certain distance.

Now does that mean its spl is lower compared to a lower qts woofer with everything else in the woofer remaining the same ?

Now it could mean that the higher Qts woofer will take more wattage before it reaches x max, however a lower Qts woofer could well have a higher X max and hence takes more wattage. Like softer is more flexible, stiffer is more brittle.
Q is compliance, which is the inverse of stiffness, so a high Q driver's suspension is "less stiff" than a lower Q driver.

The Qts values are composite values of the mechanical (Qms) and electrical (Qes) parameters. So the total driver Q is related to it's cone mass, as well as the suspension (mostly spider stiffness and a little from the surround).

High Qts drivers (think heavy cones and/or soft suspension) are used in sealed boxes because they rely on the stiffness & spring rate of the air volume in the sealed enclosure for proper tuning. Lower Q (stiffer suspension/lighter cone) drivers are used in ported enclosures since they rely on their stiff suspension combined with the box volume & port tuning for proper system tuning.

Different Q's have different responses around resonance, ie higher Q's have greater amplitude over a smaller freq band and lower Q's have lower peaks over a wider freq band. They may have equal area under the curve, but it's been a while since engineering school.....

The loudspeaker design cookbook is an excellent reference for this info, even the older editions. Pick up a copy if you don't already have one.
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Q is mainly related to motor strength, not stiffness, although if you remove Fs (and if I did my math right ;) ) there is a weak stiffness component (Cms is compliance, the inverse of stiffness).

Qes = 2*pi*Fs*Mt*Re/(Bl)^2 = Mt*Re/(sqrt(Mt*Cms)*(Bl)^2)
Qms= 2*pi*Fs*Mt/Rms = Mt/(sqrt(Mt*Cms)*Rms)

Bl is the magnetic flux in the gap times the length of wire in the gap. (Bl)^2 / Re is the electrical damping, which you will see is quite large in most drivers, such that Rms is nearly insignificant.
Rms is a lumped mechanical damping term which includes suspension, radiation, etc...

Voltage sensitivity is directly proportional to (Bl*Sd/(Re*Mt))^2 Stiffness is not a factor in SPL, but excursion capability is.
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