Hey,
well , grab the wav format specification : it's free .In general Wav file consists of a header and a data itself. containing most of the file-related data. All the "meta" data is stored in the header : file's sampling rate, whether it is mono or stereo , amount of bits per sampling etc. Data contains original signal's amplitude values...that's it. So in case if a sample is coded with a single byte , for a single channel , you can store it's value as unsigned char.Working with 16 bit samples is a little more tricky but since QString offers a great interface to work with the same 16bit unicode characters...not that hard. Once file's data is translated...plot it , there are a lot of examples regarding graphics in Qt.
P.S: there is great program that performs some great spectrum analysys : FFT Properties (you might want to use it to check if your obtained data is correct or not)