Re: 1960a mod !?
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I went to the local home supply store and picked out a nice piece of Russian birch multiply. I had it sawn to the right dimensions there too. Only cost me 10 Euro. It's the best part of the mod IMHO

. I used a hair dryer to soften the glue residue on the tolex.
That along with the new jack, wiring and foam makes a world of difference.
I hated the cab when I first got it, it was harsh sounding and had almost no bass at all. Thats why I started looking around what I could do to improve the sound. I have spend about 500 total including mod materials and got one killer sounding cab!
I am not a cabinet expert but I got the foam trick from a local guitar store guy. He did it to many speakercabinets and he always got good repsonse from the customers.
The foam is to keep the sound clear and defined. I used simple grey 'egg carton' sound isolation foam you can buy everywhere.
Trying to figure out the physics behind this will only result in much speculation.
But in high end audio speakers you will always find foam on the inside so that can't be coincidence.
I think the middle block is to keep things tight together. Guitar speakercabinets are a piece of engineering with all kinds of vibrations and frequencies that come into play we might not know about.