Here you see a 44 kHz piezo transmitter (top right) and receiver (next to it under the black rubber handle of the pliers),
The receiving side is tuned by a 330 mH inductor tuned down (permeability) by a very strong bar magnet at some distance from it, to about 80 mH I'd guess,.
Watch the scope and movement of the magnet relative to the coil.
So we need no caps, no variable inductors.... just glue the magnet in place ;-)
Inductor, and the magnet, in an IC tube, bottom left...
Circuit is very simple
[ ] ////// -|[]|- 44kHz piezo transducer from old acoustic remote parallel. bar magnet inductor in ferrite housing
Q is Ferry Hi , and the Rx side needs precise tuning to the Tx side.
Now the Rx signal at this distance (few cm, maybe an inch) is about .5 V with 200 Vpp on the transmitting transducer. These high level signals could make an acoustic speedometer more reliable, much better that 5 V PIC output pulses....
This is also the basic Doppler setup, then the Tx and Rx signals are mixed in a dual gate MOSFET, and the difference frequency says something about the speed of the receiver transducer relative to the transmitter transducer, or any reflected object in the beam. Could that be air? :-)
And the test goes on...