The question is whether the increased stiffness is audible or even measurable.
Absolutely no question that the increased stiffness is measurable.
Whether it is audible (as it is used in the sub) is an entirely different question. However If the designer wants a stiffer cabinet, he has several choices. He can make the wall thicker, add bracing, add curvature to the wall, or reduce the dimensions, it just depends on which trade-offs he wants to take.
I believe the take-away should be that HDF adds nothing unique to the performance, it is one of many alternative approaches to improving stiffness!
For that matter, why aren't subs made using injection molded plastic? Which is much lighter and just as stiff isn't it - its used in pro loudspeakers which have stringent standards and measurements, much more than any so called 'hi fi' speaker.
Which Pro Loudspakers?
I have several pro studio monitors and they are all MDF. Some (like the JBL LSR305) do have plastic baffles in front and most have the metal plate of the amp spanning the back.
I believe the reason for the plastic baffle is they can economically mass produce the shape to accommodate wave guides (my Klipsh home audio speakers have a plastic baffle).
I think pro audio puts a high value on portability, so plastic (with ribs molded in to create the needed stiffness) for weight reduction makes sense. Ideally, they would use injection- molded foamed plastic with counter pressure to get sealed surfaces with plenty of air pockets inside the plastic (to keep the weight down).
That is the thing about plastic, it can have a lot of properties designed into it (including fiber glass such as the handles often used for hammers). There is cheap basic plastic, then there are highly engineered plastics!
My best studio monitors are Focal Twin 6Be and, aside from the metal plate/heat-sink on back, they are all MDF!
The ID craze was started by Svs (and Hsu) using subs made out of sonotubes - certainly not wood. And there was absolutely nothing wrong with them.
I did not know that Hsu and SVS started out with sonotube subs - cool!
Good question!
However, it is important to understand the strength of a cylinder vs a box. This is a huge factor!
I think we intuitively understand this - consider a tube from a toilet paper roll. If you seal the far end with your hand and attempt to blow it up like a balloon, you will do nothing obvious.
If you had a similar sized (and wall thickness of cardboard) tube with a square cross section, I think you recognize that you could get the flat walls to bulge or "balloon" out!
This is why all LP gas tanks are cylindrical and truly high pressure tanks are spherical. If square, the bulging/flexing due to pressure changes would result in stress concentrations and fatigue failures at the wall edges/corners. With a cylinder the only stress is the wall being "stretched" in tension, trying to expand the circle (like a balloon expands as the rubber is stretched). That won't happen very easily, even with a cardboard sonotube. Building a box as rigid as a cardboard sonotube is no easy feat. You certainly could not expect a box made of flat cardboard the same thickness as a sonotube to be stable!
Edit: Since we are talking subwoofers, I should add that we are not just talking about pressure, but also pulling suction on the walls. However the strength benefits of a circular cross section in suction are the same as when pressurized. The important thing is that the suction is in the air so it pulls equally all the way around the periphery.
A fun demo of this (especially if you have a kid) is to take a couple of small eggs out in the yard and wrap your hand completely around them then gradually squeeze to crush them. Be sure to squeeze as evenly all of the way around the egg as you can. You will be amazed at how strong the egg shell is under this load (of course we are not very good at applying even pressure on the entire exterior of the egg). We know how easy it is to crush an egg if you press into it with your thumb, but airwaves will apply the pressure evenly.
Mechanically, pressure from the exterior is the same loading as suction from the interior. For a pressure vessel (which is much of what a sub cabinet is) it is only about the difference of pressure between the inside and the out!