I've worked in computer music/audio for years. Most people and PCs can reach 20kHz. It's no coincidence, human hearing drops off around that point and thus the 44.1kHz sample rate was chosen to match that (you can transmit frequencies at max of 1/2 the sample rate, thus 22.05kHz). But modern sound cards can reach 96 or even 192kHz sample rate, able to transmit ~50-100kKHz tones (other factors aside). Further, modern sound cards can have amplitudes expressed as 24-bit numbers, providing very high fidelity/accuracy.
So, you may be able to hear higher than 20kHz. Even if you increase your sound card sample rate, best test would be to try something analog to eliminate other bottlenecks in the audio processing. But you can easily tweak your audio settings and generate sine waves with this program:
http://audacity.sourceforge.net/