I used to have great hearing but at some point I suspect I damaged it by listening to music too loud, now I have constant slight ringing in both ears and significant loss of high frequency hearing in the left ear only. Depending on the angle of the sound coming into my ears, the high frequency hearing in the left ear still works. (With earphones or regular speakers pointing straight sideways into my ear hole I can still hear high frequencies at normal volume, but with regular speakers at a normal position diagonally in front of me, my left ear has no high frequency hearing).
Aside from speakers, actually the thing that is most likely to cut-off high frequency hearing is the Digital-to-Analog Audio converter, whether that be your computer's sound card/chip, your CD/DVD/Blu-ray player, your HDTV, your amplifier/receiver, or your speakers themselves, depending on your setup. Many DACs cut off all high-frequency sound over 16 kHz with a brickwall filter. Good speakers should be able to play high frequency sounds up to 20 kHz but some can play past 40 kHz, it depends on the tweeter technology. (Very expensive speakers won't necessarily focus on high frequency reproduction).
If your test let you hear up to 16 kHz it is likely your hearing goes beyond and your player/computer is what brickwalled the high frequency sound.
One random example of brickwalling, the original fat PS3s have a normal good-quality DAC that brickwalls high-frequency sounds (dunno at what frequency). The slim PS3s replaced it with a cheapass audio DAC that does not filter high-frequency sounds at all (technically this is a good thing but the rest of the audio DAC is also very bad and sounds like shit). This is extremely obvious to hear because in certain games, or at the PS3 system menus, you just move around and hear the artificial clicking noise play...and on the slim PS3s instead of going "click" it goes "click.....PAK!!!!!" each time. The PAK is the end of the sound snippet. This only matters if you use the analog audio out of the PS3, which many people don't use.