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: 
What makes a violin sound like a violin and not a trumpet, even though they are both sounding a note in the same pitch?

The answer is harmonic content.

A pure tone of a single frequency is essentially a sinusoidal vibration... repeated displacement back and forth which, if plotted against time, will appear as a "sine wave". When you drop a stone into water, and waves ripple out, the pattern of wave crest and trough is a reasonable approximation.

When a violin sounds a note, it is not producing a pure (sinusoidal) tone. Neither is any other musical instrument. There is a "fundamental", which is a pure sine wave at the frequency corresponding to the "pitch" of the note, accompanied by a set of "overtones" of other frequencies. These overtones occur at frequencies which are specific whole number multiples of the fundamental. The presence of an overtone at a given frequency, and its relative amplitude creates the harmonic structure of a given sound, and creates the sound you recognize as a violin vs a trumpet, or whatever.
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.