Bill Fitzmaurice wrote: ↑Thu Oct 15, 2020 6:50 am
Excursion at Fs is moot. Fs is free air resonance. It's measured with the driver literally dangling in the air. In that configuration Z is at a maximum at Fs, which results in excursion being at a minimum, but we don't use drivers suspended in the air, so it doesn't have a whit of relevance where limiting is concerned.
Why I don't tend to factor it much. Maximum and minimum excursion is based mostly on cabinet design and how it interacts with the driver's thiele small parameters - at least for bass cabinets and woofers and generally the bottom portion of the audio spectrum. For a vented box, the helmholtz resonance will usually have a minimum (and at the resonant frequency of a horn, there will also be a minimum, although probably slightly less pronounced than it is for a vented box.) The maximum displacement of a vented box will be somewhere in the middle of the pass band, probably close to what that speaker would do in a sealed box of half the size if the ports are resonating in unison. The Fs of the speaker will come into it somewhat. How much this dominates will be related to the size of the box, area of the cone, stiffness of the suspension, moving mass. I would assume it's at the point the port air is in phase with the speaker, but I am unsure as to exactly how to calculate this point, as different speakers in the same box will have a different displacement peak at a different frequency.
As a horn mouth or group of horns gets larger, the displacement and impedance curves will become flatter, though it would be rare for them to be ruler flat. As a general rule, when the acoustic resistance on the speaker is higher, its impedance will be lower and vice versa.
To answer Grant's points about kick duration, it depends how staccato the kick is. In EDM, there is a trend to attach bassline to the kick, whereas in rock music it's more likely to be a quick thump and gone. So I'm talking about what proportion of the music the main thump actually lasts. In a classic rock song with a kick every other beat - maybe one of the verses to Bye Bye Beautiful by Nightwish, this might not be much time at all. In a song that's mostly bass - like The Tunnel by Jay Cosmic, your subwoofers are almost continuously on.
The following three will heat the speaker the same on average. A continuous sine wave at thermal limit, a half second pulse at double the thermal limit followed by half a second of silence, a third of a second at 3 x the thermal limit followed by 2/3 of a second of silence.
There are limits to this. Don't expect to drive your speakers hard for a minute or longer, then rest 2 minutes - but within the realm of music tempos, the thermal inertia of the coil at least on a low frequency loudspeaker should be able to average the peaks and troughs. Obviously for tweeters, the coil is smaller and heats up more easily.
Mechanical limit doesn't work the same way. Trying to do twice the mechanical limit and then making up for it with a rest period will still damage the speaker. However, technically Xmax is not the mechanical limit, just the point at which the loudspeaker is no longer linear - whether due to suspension becoming stiffer or the voice coil not being all in the gap. (Technically with an overhung coil it's never all in the gap but a consistent length portion of it is throughout Xmax) You might notice some harmonic noise added to your clean bass notes. The real mechanical limit is a second number called Xlim or Xdamage - the total range of the suspension or coil in the gap. Note I don't recommend limiting to Xdamage as there is no margin or error whatsoever.
When I say mechanical limiter, I mean a restriction on the maximum voltage you can apply to a speaker sweeping through its pass band at which the cone won't move too much. I can usually get a ballpark figure from Hornresp graphs.
When I say thermal limiter, I mean a restriction on the maximum voltage you can apply at the speaker's minimum pass band impedance that the speaker coil can play for prolonged periods without overheating.
Thermal limit is usually "don't remain above this zone, though short duration signals can temporarily exceed it as long as there is adequate rest period"
Mechanical limit is "NEVER exceed this under any circumstances unless you like reconing speakers."
