Cats have a fairly high hearing range. [1] This means they percieve the world differently, and you can communicate with them in different ways than you can with humans.
Humans
0.05 - 23 kHz
Cats
0.05 - 64 kHz
Dogs
0.05 - 45 kHz
Bats
2 - 110 kHz
Ultrasonic noise generators
Dog whistles — absolutely work with cats, because cats have a higher hearing range than dogs
clicker training tends to be used for short-distances, while whistle training tends to be used for bird/gun dogs (and hunting dogs
it's not clear to what extent the "pest control" works — even if an animal can HEAR a frequency, that doesn't mean they necessarily dislike it. To the extent that they can tolerate it or are neutral to it, these devices can be used for purely communication purposes.
Bat detectors — People have spent a significant amount of time and effort in understanding and building bat detectors, both at the professional level (well-funded academics) and the amateur level (hobbyists who have to build their own equipment due to funding constraints). You should be aware of the scope of the information available from them, to avoid duplicating work.
one of their pages notes that ultrasonic speakers and microphones are usually VERY directional.... since the wavelength of ultrasound is ~1cm, anything that's much larger than that is going to block ultrasound, making it effectively directional
examples of what well-funded researchers get to play with:
LOTS,
$1400,
$1100,
$1000