The frequency is individual, and known as tinnitus frequency or pitch.
From Okamoto et al., 2010:
Our target notched music introduced a functional deafferentation of
auditory neurons corresponding to the eliminated frequency
band, and because this frequency band overlapped the individual
tinnitus frequency, the notched music no longer stimulated the
cortical area corresponding to the tinnitus frequency, although it
still excited surrounding neuron.
There is a dependency on "training" (from a Discover article):
Even in adulthood, experiencing new sounds can rewire the auditory cortex.
If a rat is trained to recognize sounds at a particular frequency, the
corresponding region of the tone map will get bigger.
From König et al., 2006:
To further examine the relation between tinnitus pitch
and hearing loss, we grouped the patients by tinnitus pitch
(63 kHz, 4 kHz, 76 kHz) and calculated the mean audiogram as well as the mean audiogram edge frequency for
Okamoto, H., Stracke, H., Stoll, W., & Pantev, C. (2010). Listening to tailor-made notched music reduces tinnitus loudness and tinnitus-related auditory cortex activity. Proceedings of the National Academy of Sciences, 107(3), 1207-1210. PDF
König, O., Schaette, R., Kempter, R., & Gross, M. (2006). Course of hearing loss and occurrence of tinnitus. Hearing research, 221(1), 59-64. PDF