Question

why there is an air specific sound of velocity around us? the answer must include analytics description using basic relations perspective

Answer 1

The ideal gas law sees a gas as a large number of molecules which move independt of one another, except for occasional collisions with each other or with the walls of their container. When they do collide, the collision occurs with no net loss of energy -- that is, it is an elastic collision.

The ideal gas model predicts that the speed of sound in a pure gas will be

where γ is the adiabatic constant (also referred to as the adiabatic exponent, the specific heat ratio, or the isentropic exponent) for the gas, which at room temperature depends mostly on the shape of the molecule and will have a value just a bit larger than 1, P is the absolute pressure of the gas, and ρ is the density of the gas. Using the ideal gas law, PV = nRT (with n constant, that is the number of gas molecules is constant), the equation above can be rewritten as

**## As gases around us behaves like real gases so velocity of sound is dependent on pressure of air around us so this velocity around us is air specific.

Note that if the ideal gas model is a good model for a real gas, then you can expect, for any specific gas, that there will be no pressure dependence for the speed of sound. This is because as you change the pressure of the gas, you will also change its density by the same factor. The speed of sound will have a very significant dependence on temperature and on the mass of the molecules which make up the gas.