Years ago I built a "light listener" with my son as a science fair project. It was a photocell, 741 op amp and LM386 audio amp. You could "hear" the buzz of a fluorescent lamp, the swishing of a candle flame - and the output of a TV remote. While you can't hear 38 kHz the output of something like the TV remote did end up in the audio range because the output pulses were at least several cycles in terms of time.
I toyed with the idea of constructing a bat listener so I googled and found a number of designs. One was a heterodyne system - mixed the received frequency with a fixed frequency so that the difference was audible.
Lacking any better ideas you might combine the two projects.
As already suggested, you won't be measuring the light frequency but rather the modulation of it, so to speak. Not sure this is what you want.