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A piezo tweeter is cheap so it has peaks and nulls in the audio band but almost no output at ultrasonic frequencies.
An ultrasonic piezo transducer produces an output at a narrow range of frequencies, usually 40kHz.
A TDA2822M amplifier IC is available only in a surface-mount package now and can have its channels bridged for more output level.
Half the output power of a squarewave is in its harmonics that a piezo transducer cannot produce so its output will be half what you think it should be.
My city got rid of bats by getting rid of mosquitoes with larvacide in all the drains and ponds.