How can I extract information about timbre from a .wav file. In which form can I study those features?
I think the time history of the wave file is enough to obtain all sorts of features. There are mathematical formulae to extract the features from a given time series. 

Some important features are: 


Time Domain Audio features 


(a) Short-term Energy, (b) Zero Crossing Rate, (c) Entropy of Energy, (d) Basic Statistics (short term mean and standard deviations).


Frequency Domain Audio Features


(a) Spectral Centroid and Spread, (b) Spectral Entropy, (c) Spectral Flux, (d) Spectral Rolloff, (e) Mel-Frequency Cepstrum Coefficients, (f) Chroma Vector

More details regarding audio analysis can be found in this book
https://www.elsevier.com/books/introduction-to-audio-analysis/giannakopoulos/978-0-08-099388-1

If you have enough data, using these features you can build a machine learning model to correctly classify an unknown sound.