Amp frequency requirements for super tweeters?

I bought a nice pair of super-tweeters here that play from
20KHz to 40 KHz. Came with a test tone disk. I can hear
up to the 12KHz tone, but nothing any higher. In other
words, I hear nothing coming out of the super-tweeters.
Getting older sucks. ;~(

The question is really more about the amp than the speakers.

The answer is 'yes' its useful to have bandwidth well beyond the traditional 20KHz. This is not because there is any significant information up there, its because wherever the amp has a rolloff, it will cause phase shift issues down to about 1/10th the cutoff frequency.

So if your amp rolls at 20KHz, there will be phase shift components down to about 2KHz. The ear cannot hear phase very well with individual tones, but it does use phase for image location. IOW this is easier to hear- an amp with more bandwidth will have a better soundstage. You don't need the speaker to go to 20KHz to hear this effect.

In other words, regardless of your hearing's upper limits, the high frequencies in live music have a very real effect on what is going on at the lower, more "audible" frequencies, and this goes a long way in explaining why 20KHZ shelving on "red book" CDs can sound somewhat less alive (and why LPs, with their much higher frequency range can sound so good). I find that digital with a good up-sampling DAC and a wide frequency tube amp help make the world a better place.

^^Yup!

It's been a while, but didn't Whest come out with a component that was to help meant to address that very issue? And if so, would it make sense to go with a super tweeter, or a component like Whest makes?