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.
Very few sounds you hear are regular vibrations at a single frequency (i.e. *monochromatic* sounds). Rather, most sound-producing objects will cause vibrations in the air at many different frequencies.

Mathematically, one can apply the [Fourier transform](http://en.wikipedia.org/wiki/Fourier_transform) to the function that describes the vibration over time. The result is a function that describes how strong each frequency component is.

Many instruments are decently approximated as consisting of a *fundamental* pitch and a discrete sequence of *overtones* on top of that, where the frequencies of the overtones are nice-looking rational (often integral) multiples of the frequency of the fundamental. Which overtones are present and what their relative strengths are comprise the primary components of the [*timbre*](http://en.wikipedia.org/wiki/Timbre) (characteristic) of the sound. A C# will have the same fundamental frequency of $466\ \mathrm{Hz}$ or so on both a guitar and a piano, but the strengths of the overtones (such as at $932\ \mathrm{Hz}$ or $1398\ \mathrm{Hz}$) will be different.

By the way, if you have a broad continuum of frequencies present at approximately equal strengths, the result is known as *noise* (a technical term, yes). There are certain standard types or [*colors*](http://en.wikipedia.org/wiki/Colors_of_noise) of noise depending on the specifics of the spectrum of frequencies.