Vehicle Jerks to Subwoofer Beat While Accelerating

The strange thing though is that with the factory alternator it worked just fine for several years.. and now it’s been replaced with a new one too..

But since everything worked fine for several years with the factory alternator and battery without issues, and since both have recently been replaced with new ones, is there anything else that can be the cause of this voltage drop that I should be looking at?

Any recommendations on which connections to check and where? Aside from basically the connections to the battery, amplifier connections, capacitor connections..

I will check and reseat all the connections at the battery, amplifier, and capacitor. I also have a circuit breaker instead of a fuse, I will check the connection there as well. I have been advised to check voltage at the battery and amplifiers under no stress and stress.. I will report those numbers back once I’ve got them as well

Ok, so I did some testing with a good friend of mine (whose pretty good with sound systems and electrical stuff) and here is what we found:

With the sound system off:

Battery: 14.3v

Amplifiers, capacitor, circuit breaker: about 14v

With sound system on and bass turned to full and volume blasted (lowest values which were hit):

Battery: 13v

Rear Fuse Panel: 11.2v

Amplifiers: under 12v (between 11-12)

We also noticed that the system was installed with a 4 gauge wire which was not even independently run to the battery in the front, it is piggy-backing off the rear fuse box power which also has a 4 gauge running to the battery. When I was at land rover today, the service manager confirmed that everything behind the fuel tank and a lot of stuff related to fuel pumps, injectors, etc. are controlled from that box and it's basically a small computer which also needs power and, as we suspected, that could likely be causing the jerking.. See image: https://www.dropbox.com/s/wwku1vfuj10kdc2/IMG_9160.JPG?dl=0

The service manager did say that people normally run a second battery in those trucks.. and the Bentley's and others come stock with 2 batteries as well and one runs the electronics..

My friend said that he feels that the capacitor is probably shot as well and replacing that with a higher powered one (he suggests 10 or even 20 farad, even though I think a 3 farad would suffice) may help with the issue but recommends also running a 0 gauge power wire to the battery (adding a second battery is ideal of course but that is way too much more work/cost)..

Let me know your thoughts..