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A crossover is device that sends proper frequencies to speakers which would be best able to reproduce that particular signal. It's basically a filter circuit. There's 2 types. A highpass (which is a capacitor, looks like a small tube) or lowpass (which is an inductor and is a wound coil). A combination of the two would be called a bandpass. So for your typical 2 way component system, let's say you have a crossover point of 3500Hz. Above 3500Hz (highpass) would go to your tweeter and below 3500Hz (lowpass)would go to your woofer. The dB per octave is the slope which is the rolloff the the speaker or how quickly the sounds filters out. If your crossover was 3500Hz at 12dB per octave (octave is a halfing or doubling of a note, at half an octave lower, 1750Hz, your tweeter would be playing a 1750Hz note 12 decibels softer than at 3500Hz. The crossover doesn't make the speaker just stop playing at a certain frequency, rather it starts to attenuate it until it barely audible. In cheaper speakers, crossover are only used on the tweeter. The woofer rolls off naturally in the top end.
The crossovers I described are the passive type. They deal with an amplified signal and is connected AFTER the amplifier. The other type is the electronic or active type, which occurs at line level, BEFORE the signal is amplified. These active crossovers can either be a separate unit or built into the amp. You will need both type in your typical system, since the passive crossover will not be able to separate the frequencies between your stage (front speakers) and your subwoofers. You don't want to send too much bass to your front speakers because that's what your subwoofers are for.
Hope this helps..
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