Keeping it simple, is it possible to use sonic waves to apply rotary force to an object? And, if so, would it be possible to provide enough power to it via conventional battery tech?
Well... yes. And also, no.
Engineers have actually attempted this, with a degree of success.
There's an article here: http://www.themarysue.com/real-sonic-screwdriver/
Hypothetically, it is possible. In practise it can be achieved with large bulky equipment operating on a lightweight object which is responsive to the sonic waves.
It's a long way off being able to open doors and program computers, but there is hope.