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Why is there a hump in a Butterworth crossover and a flat response in a Linkwitz-Riley? Shouldn't two sources -3db down each combine to add 3dB to create a flat response and two sources that are -6dB down each add only 3dB to create a dip?
 

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It would be true if the 2 drivers (or sub and mains) are perfectly in Phase at that frequency (which is not likely to just happen without careful design.)


If there is a phase difference there can be some destructive interference which can cause subtraction rather than addition.


This is why amps built for subs have a phase switch of some type that can make finite adjustments or just reverse phase (which can also be accomplished by switching the positive and negative leads)
 
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