How can a changing signal be Fourier transformed?
You are correct that it is often broken up into chunks. There are multiple ways to combine those chunks (Google: fft overlap save).

It is often important to window the data (again Google: hamming window fft). One critical reason to do this that gets to the heart of your question: the fft assumes the chunk you fed it continues infinitely forward and backward in time. Obviously an audio file does not have this property.

For your example you might want to chunk your audio file into groups of powers of 2 like, 1024,2048, or 4096.