This worked great. Like others on this list, I was not able to see an actual tear in the paper portion of the speaker. But by watching closely with the music playing I could see that the foam around the outside was flapping around at the very outer edge where in connects to the metal frame. I put a healthy dose of glue all around the outside of the foam by the metal and the inside of the foam where it connects to the paper cone for good measure.
I have a 2001 LS that I purchased in 2005. I think the stereo was fine when I first purchased, but eventually it started cutting out when the volume was too high (which I thought was something in the amp, rather than the speakers, so I lived with it for the last few years). In the last week or so, the woofer "blew" and luckily I found this post before buying a new speaker. This quick fix corrected both the "blown" speaker and the cutting out issue that I had.
The bass has never sounded so good.