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: 
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.
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.