Driving high voltage to ultrasonic transducer with Arduino
Judging from the Captain Obvious position, the best approach will be to have a separate DC power supply for the transducer, with arduino driving the transducer through an H bridge. Transducers have relatively complex pulse response as they are and adding another resonant circuit behind it is definitely not going to help with all kinds of auto-oscillatory behavior in the circuit.

If this is out of question, you will have to do some pole-zero analysis of your network using the actual transducer model (because it definitely needs a more complex filter network there).