I do like listening to sweeps to listen for resonances, rubbing things, broken stuff, unsecured wires, or lost items that have fallen into ports. For instance, I just have a woofer that had a surround that wasn't glued properly:
FFLOTSAM (Fabricated From LeftOver Things Studio Active Monitor) Active DSP speakers, for testing a few ideas I had some stuff lying around; a few random Baltic Birch-ply panels, some countertop material, a few cans of partially used brown spray paint, and some not-too clumpy spar varnish (that...
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I could hear it in the built speaker but couldn't localize what was wrong with the driver, and the surround really laid flat while I inspected it so I didn't see that half the glue was missing from the surround. But gosh could I hear it during a sweep, the surround's floppiness would modulate as the frequency was swept drew my attention directly to the problem. I'm a little embarrassed it took me so long to trace.
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If you read the post, you will see the unglued surround barely showed up in the frequency response traces compared to the good driver! You had to compare distortion, which had peaks at all of the frequencies where the surround started burping. I guess my point is, I like sweeps and feel it's one of the few audible diagnostics where I trust my hearing.