There are many things that could account for the distortion you are describing, and I don't know if it is efficient to try and diagnose this. It could be due to the eq distribution of the content as well as overall volume. Seems better to me to just start over with a simple sine tone and see if that can work.
Are you generating the sounds procedurally or using prerecorded cues (e.g., wav, ogg or mp3)? If making the sounds via a sine function, it is good to remember to put in fade-in and release intervals so the sounds don't make an ugly click when they start or stop. For example, a bell-like envelope with a short attack (3 millis, say) and longer decay (250 to 333, ballpark starting point) could work without sounding unpleasant.
It seems to me a quickly repeating note (e.g., tapping two or three times) pitched around 1 kHz would probably be in the ballpark. This tone would be within speech frequency ranges, at the upper end (for vowel formants, though not as high as the fricatives or sibilants which are often shorted in low-quality audio) where it would grab attention. A little note pattern could also work, e.g., C7, E7, C7.
There's a free little Java tool made to make utility sounds--DinkMaker. If you download it (it is small, I wrote it, requires Java 8), I'd recommend trying the file named DinkA6, and playing around with the settings. The envelope is a little short--I'd lengthen the release.
It is easy to try different frequencies with this starting patch, and find out what different pitches sound like and what their frequencies are. The tool will let you export to wav if you come up with something that you like. A multi-tone cue would either be played procedurally, piece by piece in quick succession, or the parts could be assembled into a single cue with Audacity and imported and played via a single command.