Question: **What are those characteristics by which every sound can identified uniquely?**

For example, pitch is one of the characteristics of sound, but let’s say a note C# can also be played on a guitar and piano with same pitch but the resulting *sound* that we hear is different so what are those characteristics which defines every sound.

Answer: 
The entirety of the wave train is involved in the perception of [timbre](http://en.wikipedia.org/wiki/Timbre) and it is not reducable to a few easily measurable features. There are entire books, including one by Helmholtz, investigating the characteristics of sound and how it relates to perception. I like *Music, Physics and Engineering* by H. Olson.

Often the power spectrum of a given sound is used to help analyze the timbre of notes; the relative magnitudes of the different harmonics, and the degree to which their frequencies differ from the theoretical ideal are a good starting point. However, these Fourier transform based approaches are not complete in that they typically do not address the perceptually salient features such as note attack and decay.

Another approach to take is to examine how synthesizers generate sounds; for this I recommend checking out the Sound on Sound article series [Synth Secrets](http://www.soundonsound.com/sos/allsynthsecrets.htm).
Two waves never mix up together. They just add up when they meet while travelling along the same medium. This phenomenon is called interference. But they still retain their own properties and shapes, and return to their individual shapes when they divide. May be, brain uses this property to recognize individual sounds.

Look at [these](http://www.physicsclassroom.com/class/sound/u11l3a.cfm) animations for better understanding.