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: 
For a long time, timbre was believed to be based on the relative amplitudes of the harmonics. This is a hypothesis originally put forward by Helmholtz in the 19th century based on experiments using extremely primitive lab equipment. E.g., he used Helmholtz resonators to "hear out" the harmonics of various sounds. In reality, the relative amplitudes of the harmonics is only one of several factors that contribute to timbre, and it's far from sufficient on its own, as you can tell when you listen to a cheap synthesizer. Flicking the switch from "flute" to "violin" doesn't actually make the synthesizer sound like a flute or a violin enough that you could tell what it was intended to be.

A lot of different factors contribute to timbre:

* relative amplitudes of the harmonics
* the manner in which the harmonics start up during the attack of the note, with some coming up sooner than others (important for trumpet tones)
* slight deviations from mathematical perfection in the pattern $f$, $2f$, $3f$, ... of the harmonics (important for piano tones)
* the sustain and decay of the note (guitar versus violin)
* vibrato

Some sounds, such as gongs and most percussion, aren't periodic waveforms, in which case you don't even get harmonics that are near-integer multiples of a fundamental.

Because there are so many different factors that combine to determine timbre, it's remarkably difficult to synthesize realistic timbres from scratch. Modern digital instruments meant to sound like acoustic instruments often use brute-force recording and playback. For example, digital pianos these days just play back tones recorded digitally from an acoustic piano.
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.