Hello folks, I need your opinion before I spend money for nothing

depending upon box volume a PRV 10FR300 with whizzer cone-- could be useful in a situation like this - I wish is hasd lower qts but for the money its good. It needs a tweeter above 7-10KHz.
 

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Is it possible to reduce the box size by adding, like, Styrofoam ''peanuts'' or a pillow in the bottom of the speaker box ?

Never tried myself, but hard foam like styrofoam should work. PET bottles fully filled with water are nice for experimenting.
Pillows are usually filled with polly wadding which acts like absorber, so not suitable.

Why do you want to reduce the volume?
Your box volume is a good match to Alpha 10A.
 
The speakers box are a little boomy, probably because the volume is to big for the speaker ?

Alpha 10A Qts is little high, reducing the box volume won't help
Try this:
Move speakers 1-1,5ft away from rear wall
Cut the subwoofer lower: 70-80Hz
Add 1lbs polyester wadding in each box, for absorption.
Sorry for this, but are you sure tone controls on your amp are off

And markbakk may be right, this could be your room acoustics issue
 
I'am puzzled too. Layout looks correct on your pictures.

Have you removed the enamel before soldering the coils? Some enamel types don't allow direct soldering.
Also check for cold solder joints or possible shorts. Maybe something moved accidentaly during installation.
 
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