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This question is related to sub-woofers in general. Currently i use MTH-30 DIY box, its tapped horn and it is possible to see driver when working, and hear the distortion.

First, i have used this driver with some 120w DIY amp, and i can get some power until speaker begins to sound distorted.

Then i have bought amp with 170w channel @ 8 ohm. I can now get more spl, but when amp is near clipping, bass begins to sound like membrane is flapping.

I know with current driver this design should be able to receive about 300w@8ohm, or about 49V.

Is it possible that this distortion sound is happening because limits of the amp, not the speaker? Amp is not clipping (clip light doesn't come on, if this is relevant), but is it possible that amp simply cannot control speaker at upper limit of declared power ?

There's quite a few things that could be wrong here. For starters, most clip lights only indicate that the clip light is on. There's a correlation with clipping, but there's no causation.

Second, the declared power of an amp needs to be taken with a grain of salt. They are often somewhat "optimistic".

Third, it could be something earlier in the chain that's clipping.

You need an oscilloscope to know for sure if the amp is clipping, and where.