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my 2001 LX has had really poor sound for a while. it got worse over the last few years. It sounds like there is a lot of distortion in the speakers. I wonder if this is coming from the radio (it has the factory radio/casete and I added the honda OEM CD player back in 2001 when I bough it). Or it is more likely the speakers?

 
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Connect some 'known good' speakers and see how it sounds

 
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Most likely the speakers. I personally found that replacing the OEM front speakers made a noticeable improvement. Probably the first upgrade to make on the audio.

 
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Agreed. Now, don't worry about newer, aftermarket speakers sounding "louder" than your cheap stockers, because they won't. The stock ones had very low power handling, and their Sensitivity(dB) is quite a bit higher @ 1Watt of output. Honestly? If you upgrade the speakers, might as well go ahead and upgrade to an aftermarket head unit as well? Possibly replace the stock wiring (and the crappy connections that have degraded over the yrs), etc, etc. I could go on-and-on. But that's just me

 
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your civic is equipped with 6 1/2" speaker all around two in back and two in front and they are not at all a good quality meaning they are weak but if you replace them with good two way or three way speakers you will see the difference at once. Hope this help.