My comment also contains the phrase "super interesting". Now I wonder where that comes from. However, technically to find the frequency in question you could take a white noise generating sound source and connect that to an EQ with an audible dB boost in a narrow range and sweep that through the entire frequency range until you tune it to match the noise in your ear. To create a filtered noise track you could apply a high pass filter and a low pass filter in combination to "bracket" that range and create a narrow band of noise. Enjoy the silence, and check out Aphex Twin (start with: selected ambient works 2). :)
For that I used Reason (digital audio workstation), create a single sine wave synth and played on the keyboard until I found the right frequency. I already knew my tinnitus was a low one for me (sounded like a mains hum) so was looking in the 20 - 200 Hz range.
You don't need the exact frequency really, just create a white noise sample in Audacity. The filtering just helps to allow playing the noise at the lowest overall level possible while still being effective in suppressing the tinnitus.
I think I could have achieved the same filtering using one of those hi-fi equalizer modules that were all the rage in the 80s and 90s.
I tried to do something similar, but I discovered that my hearing range ends at a lower frequency than my tinnitus' apparent frequency. It's interesting that my body is synthesizing a signal higher than I can actually hear.