Large Advents (1974) woofer pops with deep bass.

Uh, considering they're almost 50 yrs old you may want to consider buying something newer ...

Yea, if the speaker driver is 50 years old, it probably needs new surround’s, however you can get replacements online usually at pretty good prices. Check out Dayton. I’ve used their woofers in projects a couple of times and been very happy.

All the best.

The LA of 1974 would have a Masonite ring with a 9” paper cone in a 12” basket, designed that way specifically to prevent bottoming.  So either the inverted foam surround is perforated or there is another air leak somewhere…or you are overdriving them.  They should handle a 125W amp easily, but you may have more.  Are you boosting the low end?  Don’t. People used to stack pairs to increase their output.  They had impressive bass but there are limits!

Bad surround may be the issue & hopefully no permanent  damage has been done., There are a few surround re- foaming kits available on eBay for short $ for the original Large Advents that are worth trying & because there were so many of these speakers sold, there’s probably entire woofers available also. Jensen then distributed & I think made a replacement woofer for it that has no Masonite ring & a black metal frame that is a perfect fit & works very well. I owned a few of the Advents back in 1974 ( one pair & then a stacked pair) & again later on in the 90’s ( left in a home I bought!). 
 

I blew a few woofers playing them at stupid high levels but overall they’re were a great speaker in its day for $210 /pair in Walnut cabinet). For the equivalent & $1200 or so today, there are speakers w/ better high end & image better but few if any w/ better bass. They are warm & musical & their faults are more omission than commission.  Get them fixed & enjoy a true classic!
 

Unfortunately, these speakers, as good as they were in those days, are really not very good.  BIG SURPRISE to me when I opened my shop in 1974 and thought they were AMAZING until I put almost any other speaker next to them 

Box speakers have come a LONG WAY since then, no disrespect to Mr. Kloss, so you might be better off buying (even used) a newer speaker than putting money into fixing those.

Cheers!