*Sorry for the double post. Hit Submit instead of Preview, by accident*
For $200 on speakers you might be able to pick up a decent set for the fronts and rear. Do you have any idea what the stock speaker sizes are for your car? Probably, 5.25's in the doors, and 6x9's in the rear. Time to find out... be back soon....
http://www.team-integra.net/sections/articles/showarticle.asp?ArticleID=248
Alright, apparently a '96 Integra has 6.5" round speakers in both the front doors and rear side panels. Does that make sense? If so, that's a great place to start as 6.5's are able to produce more bass than the usual 5.25's like I had stock in my Elantra.
Look for 6.5" component speakers for the front, and 2-ways for the back. I'll go looking...
MB Quart DSG 216
6-1/2" 120W 2-Way Component Speaker System
http://www.onlinecarstereo.com/CarAudio/ProductDetail.aspx?ProductID=17716
Sony XS-GTX1620S
6-1/2" 260W 2-Way Component Speakers
http://www.onlinecarstereo.com/CarAudio/ProductDetail.aspx?ProductID=19494
Pioneer Premier TS-A642P
6-1/2" 4-Way 280W Car Speakers
http://www.onlinecarstereo.com/CarAudio/ProductDetail.aspx?ProductID=17680
Component speaker setups are those where the tweeter speaker is separate from the main speaker. This, generally, results in a
much better sounding speaker configuration. However, they cost more to install because you need separate mounting locations for the tweeters, and the cross-over which only allows high frequencies to reach the tweeter.
You also want to take into consideration the frequency response of the speaker. The MBQ has a response as low as 40Hz, where the Sony has a response as low as 28Hz. Lower isn't necessarily better, but it can be if the speaker plays that low note with precision. Having speakers that are able to play a broader frequency range should make your system sound better. But you might give up volume for quality, which I think it a better route to go anyway.
I need to know the model number of the subwoofer, as much as you know, to properly suggest an amp that would work. You may also consider buying a Multi-channel amp to play the 4 speaker channels, and a separate mono amp to power the subwoofer. But this'll likely cost you more than your aiming to spend. I'm sure you could get away with running the 6.5" speakers off the head-unit power, but you're not getting the full potential from the speakers in that case.
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