The earth would definitely have been correct and the permenant live just requires a switch of bullets in the stereo loom
Further to your comments about the speakers not handling the power, it’s not so much the speakers as where they are mounted, go look at your house hifi speakers and tell me if they are mounted in a sealed, solid enclosure or a piece of tin with more holes than Swiss cheese? One of my descriptions resembles your van and one is the most efficient way to mount speakers
You will also find the amp in your stereo is only 4x10-12watts rms (ignore any bull claims of 4x45wats peak on a good day with a trailing wind) so in reality it’s probably a combination of the amp distorting and a poor mounting location for the speakers leading to distortion, my point is that even if you upgraded the speakers to say a 6x9 the bass may get a little better, the mid and treble would definitely get louder
in reality you’d be better off for some audio quality upgrading the stereo to an alpine or pioneer with in built high pass crossovers to allow the four speakers to do something they can do relatively effortlessly and popping an active sub somewhere as it will be the bass that distorts first
The other way to improve matters is to sound deaden the areas local to the speakers and seal them off as best you can, this will improve the mid bass response by a good chunk and warm the sound up no end and also reduce some rattles in the process (plus your front doors will sound like a Lexus when they shut instead of a tinny French car
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