Displacement and Xmax

[mfenske 10+ year member]

Something I've always wanted to know as it relates to speakers is the relationship of displacement. I think about it like an engine where it's bore*stroke. So would it be reasonable to assume that a single woofer that moves 3x further than a trio of woofers that moves 1/3 as far would achieve the same output given the same amount of power applied and sensitivity?

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[Dmac1991]

Same size woofers?

Would the trio of woofers have optimal enclosure specs?

Or are you asking something like 1 18" woofer compared to like 3 10s?

If the 3 subs are given optimal space, compared to the single woofer, I'd say the trio would have the edge at being louder. Have to figure in impedance rise due to heat and everything else on that single woofer, even with 1/3rd of the xmax of that single woofer

 

[mfenske 10+ year member]

Same sized woofer. I'd figure if a 12" sub with the same cone area moves 3x further than 3 12" with the same cone area it would be the same output?

 

[akadj 10+ year member]

Same sized woofer. I'd figure if a 12" sub with the same cone area moves 3x further than 3 12" with the same cone area it would be the same output?

This question is asked a lot and is not easy to answer.

It depends on what frequency you are going to play?

If for SPL only you would be tuned in the mid 50hz up to 80hz and xmax is not an issue. Also you have the least amount of cone movement at you enclosure tuning so again you'd lower the need for high xmax... That is until you start throwing gobs of power like 10kw per driver.. My atomic ELE 15's with 7000 watts per woofer only moves around half its total xmax when played at 60hz.

let's say your box is tuned to 60 hz.. And you play 30 hz just for the fun of it.. Your woofer excursion would be 4x more then the same woofer in an enclosure tuned to 30.. By playing half the box tunning you quadruple your excursion at the same power... See where I'm going with this.. Just because a speaker moves air doesn't mean it has a high output or SPL

In the world of SPL Its all in the box/vehicle/endless testing!

 

[T3mpest 10+ year member]

Same sized woofer. I'd figure if a 12" sub with the same cone area moves 3x further than 3 12" with the same cone area it would be the same output?

Are we talking in a sealed box and holding frequency response constant, then yes those scenarios will give you equal ouput, but things get funky as AKADJ pointed out down below. However, here are the basic points to understand

1.As you go down an octave (halfing frequency) to keep SPL equal you need to move 4x as far.. So if a speaker puts out 100db by moving 10mm at 40hz, to put out 100db at 20hz, it would need to move 40mm.. As you go upward the opposite happens, so higher frequencies need less xmax than lower ones. Generally speaking most speakers are NOT xmax limited above 40hz, even 10-15mm of xmax can be painfully loud (literally) at those frequencies and often the power levels needed to get a speaker to even those levels is enormous.. Ports have a similar effects as I'll outline below. However for reference, I have a very powerful 21 in my car right now with 15mm of xmax and without at least 2k on tap, you'll never reach xmax at any frequency above 30hz.. If you port it and your talking 40hz and higher, you'll likely never see xmax until 4k or so of input.

2.Motor force helps determine how much cone movement you get from a given amount of input power. This is why subs with low xmax can still be loud, especially ported. When a speaker is ported, the woofer and port are out of phase and the port fights the cone, damping it's movement. This reduces cone excursion, however, since that's where the port is most sensative, you get a lot of output from the port with very little movment from the cone.. That's why 30mm xmax weak motored subs still may not get as loud on a meter as a 15mm xmax high motor force sub. The trade off is that a sub with a high amount of motor force relative to it's weight has a high resonant frequency, or fs.. This makes it less effecient at playing low notes in the first place, which is why they excel in ported boxes. Sealed the roll off very fast.

3.Power compression and BL compression effect the actual power levels needed to reach these cone excursion levels.. To get that single 12 to 30mm of xmax might require on paper, 900 watts. However as the coil heats up it's impedence rises, reducing the power your amp can supply. In addition as the coil leaves the gap, the motor force of the speaker drops. As I mentioned in point 1, that means your speaker now needs MORE power to continue to move further. So now Instead of 900 watts a modelling program would tell you is needed, it actaully needs 1600 watts AND your 2000 watt amp has heated the coil up so much your amp can only put out 1500 before clipping //content.invisioncic.com/y282845/emoticons/biggrin.gif.d71a5d36fcbab170f2364c9f2e3946cb.gif So often times, more cones moving less distance is more effecient overall because both those effects are minimized.