The Fourier transform assumes the signal is analysed over all time  an infinite duration. This means that there can be no concept of time in the frequency domain, and so no concept of a frequency changing with time. Mathematically, frequency and time are orthogonal  you cannot mix one with the other. But we can easily understand that some signals do have frequency components that change with time. A piano tune, for example, consists of different notes played at different times: or speech can be heard as having pitch that rises and falls over time. The Short Time Fourier Transform (STFT) tries to evaluate the way frequency content changes with time: The diagram shows how the Short Time Fourier Transform works:
Each frequency spectrum show the frequency content during a short time, and so the successive spectra show the evolution of frequency content with time. The spectra can be plotted one behind the other in a 'waterfall' diagram as shown. It is important to realise that the Short Time Fourier Transform involves accepting a contradiction in terms because frequency only has a meaning if we use infinitely long sine waves  and so we cannot apply Fourier Transforms to short pieces of a signal.
