Do some tweeters intentionally have a peak at around 10KHz?

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I don't know if this is true but some tweeters have a slight depress at around 3K - 7K, but then have a slight peak at around 10KHz. I think sibilance is in the 3K - 7K region. At around 10Khz, it's not sibilance but more like what audiophiles call "air". So I don't know if this is intentionally done to add an extra sense of "air" without increasing the sibilance. I am not sure I like this approach though since I think any intentionally emphasis in any freq. response would make the sound less natural.
 
Interesting question. I cannot answer it, but I know this: many tweeters are 1" soft domes. Those have a resonance at their lower cutoff (~1 kHz) at which the dome moves as a rigid body. This can cause a bump at that frequency. Modes of the dome itself start at 6 kHz if I remember correctly, so one of these could cause a peak at 10 kHz. Those usually are well damped, but still one of them can show up in a graph. Furthermore, above ~5 kHz a 1" dome starts to beam, increasing the on axis sound level as those high frequencies are forced forward.

A broad bump at 1 kHz and a narrow one at 10 kHz somewhat matches your description.
 
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The Vifa / SEAS tweeters used in the 1990s Snell Acoustics speakers had a response peak in the vicinity of 10kHz. FWIW...

1091Snefig2.jpg


"Snell E/III, anechoic response on tweeter axis at 44" (black), corrected for microphone response, with individual responses of the tweeter (red), woofer (blue), and port (green), measured in the nearfield below 300Hz." (From a review in Stereophile Magazine)

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Broad bumps at 1 kHz are due to a higher Qts which in itself is not an issue if you know how to design HP filters. An example is SS D3004/604000. Standing waves at 10 kHz calculate to 1,7 cm so maybe not adequately stuffed rear chamber.
 
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