Strange noise? A lot depends on how well the woofer was designed and made. There's often a very audible sounds that happen when the speaker is driven harder, in particular from the air movement behind the spider. Or the voice coil could bottom out in the magnetic gap creating a very hard not to hear hammering sound. Longer than necessary wires that connect the voice coil to the terminals can slap the cone at high excursion.
The wedge micrometer:
credit to Linkwitz Lab: http://www.linkwitzlab.com/images/gra...
Even without the wedge micrometer it's a good idea to run this test to see how the woofer you want to use performs.
When I say you can use this to design your speakers, I mean you can use it to define the limitations - just how far the speaker can be pushed before it starts making something other than music.
Don't use this to replace the published Xmax of a driver.
Instead, use this to do a reality check on the speaker design and get an idea of the amount of usable output you can get.
Most woofers are over-driven on transients and will distort. But it's the amount and severity of that distortion that matters.

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