How is it possible plotting frequency vs. time in audio? Something which makes me confused is how it is possible to create plotting of frequency vs. time domain.

Isn't time domain is opposite of frequency domain and the only way is to plot amplitude vs. frequency or amplitude vs. time?

What is the main target of this plotting time vs. frequency of audio signal?
For traditional signal processing, time and frequency are dual variables, linked through Fourier transformations. This strong linkage yields a balance, sometimes called Heisenberg–Pauli–Weyl uncertainty inequalities. In everyday words, one could not be arbitrarily precise in time location and frequency determination. One cannot determine the frequency of a single sample.

However, in audio, meaningful information is usually carried by chunks of time, or collections of samples. So very often, people perform Fourier-like transformations over those consecutive or overlapping time chunks. They obtain information on how frequency contents evolve over time. A lot of specific methods, termed time-frequency analysis, have thus been developed, to provide  us with useful algorithmic tools to perform such analyses. They are legion: oversampled filter bank, spectrogram, Wigner-Ville, Choi-Williams, reassigned versions, S-transform, wavelets, etc. 

In the tutorial: Time-Frequency Toolbox For Use with MATLAB (150 pages, no less), there are many comparisons. On a piecewise regular signal (sine then tone and linear chirp), they provide the following comparative plots that you can reproduce for your purpose:







One uses them  in audio for several reasons: to  analyze stationary parts, detect the onset of certains frequencies or harmonics, detect hearable information. Such techniques are at the very heart of mp3 audio compression for instance.