Sometimes we say a station is at 9680 kiloHertz (kHz)
Another time we say this station is on 31 meters.
What gives?

Boy, you got a lot questions!

9,680 kHz, or 9,680,000 Hz, is the frequency of the radio signal, equal
to the number of radio waves that pass a point, or enter one's
antenna/radio system, in one second.

31m is the approximate wavelength of that radio wave at that frequency,
and can be used to refer to all frequencies in the 9.5 to 9.9 MHz band
(nowadays extended as far as 9.2 and 10 MHz at the ends). In days gone
by, many old radios (and old timers) identified their location on the
"dial" by wavelength; some stations still use both frequency and
wavelength in their station IDs. The use of digital readout has almost
obviated this nomenclature, except for those who use boatanchors or
other cool old-time equipment.

As it turns out, a wave at frequency 9,680 kHz is almost exactly 31m
long, and almost the precise "center" of the band.

My question is - do you really want to know, or is this a test?

Or, are you just trying to say something on-topic (I admit, a
significant feat for anyone who is a part of this bunch...)

Bruce Jensen