For audio capture and playback, portaudio comes to my mind.
For audio processing, STK looks promising.
Have a look at this related question too: Can anyone recommend a decent DSP/speech library in C++?
I recommend these three libs:
very easy to use and friendly for general signal processing Aquila-dsp
strong lib for audio signal processing although hard to use and it's very big and complicated for beginners: CLAM Project
another one I have no experience about it, is worth considering though. tspl
