How do I read and write frequencies to a .wav file? C++

I'm trying to come up with my own method of transmitting SSTV. Right now, however, I need to figure out how to read and write frequency data from a wave file.

As far as I have been able to decern, wave files store the sample rate and amplitude of the audio, not the frequencies present in the file.

So to read frequencies from a wave file I'd need to perform a Fourier transform on the amplitude data. To write to a wave file I'd need to perform a reverse Fourier transform and write the amplitude data.

Optimally, I'd like to store the frequency data in an array.

I have no idea how to go about doing this. I haven't been able to find a good library that can do this.