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Double Bass Lightweight Practice Cabinet

I wanted a small, lightweight cabinet to use at rehearsals with my G&K MB200 head. To that end, I gutted a practice amp, converted it to a sealed enclosure and added a reasonably priced, 8" 8 ohm driver.

I'm satisfied with results. However, if I turn it up I hear some over-excursion when I play the open E string or the first 2 or 3 stopped notes. It's not a big deal because I can get more than enough volume for its intended purpose. I tried running through a Baggs Para DI to see if the build in HPF (70 hz) would help but it didn't seem to make any difference. If I replaced the driver with a 4 ohm speaker, would it lessen the over-excursion? Or, is it more a function of the low frequency, rather than power handling?

The frequency response is 70hz-xxx. As I understand it, the range represents the frequencies that the speaker can reproduce at a reasonable amount of distortion, not the absolute range.
 
Specs for drivers do not give you the full picture. Really good bass enclosures take careful calculations to get them sounding great. Different enclosures with the same speakers might sound entirely different based on several parameters. So essentially, it doesn't always work out to put a speaker in any old sealed enclosure and expect a good result...sometimes it does work though....just not in your case :/
 
Try a HPF-Pre ans set it to about 100 Hz or higher.
It depends on the steepness of the Baggs HPF (6 dB/oct or 12 dB/oct) how much effect the filter will give you. The HPF-Pre has 12dB/oct. with variable frequency.

If you want to stay with your preamp use a driver with a resonance frequency (about 50 to 60 Hz). I'm afraid you will only find them in 10" or 12" speakers. But you will loose highs with larger speaker cones, that's the drawback.