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Tweeters are designed to handle the very highest of audible sound (starting at about 2000 Hz all the way to 20, 000 Hz and beyond). As you listen to music, most of the high percussion (like cymbals) is covered by tweeters. Tweeters need to move very fast to reproduce sound waves that can be less than an inch in wavelength. Because these wavelengths are so small, tweeters are very directional. High frequency response will usually taper off as you move 'off-axis' from a tweeter.
Be nice to your tweeters. When you drive your amplifier into audible distortion, tweeters are usually the first to blow. If you have blown your tweeters, you should replace them with the original manufacture's replacement tweeters—that is, if you want to retain the sound you were enjoying.