Question

Why does not the speed of sound depends on the pressure of the air?

Answer 1

See below

Explanation:

The original (Newton-Laplace) equation for the speed of sound in a fluid included a reference to the pressure of the fluid :

• `c = sqrt((gamma P)/rho) qquad square`

Using the ideal gas law:

• `PV = n RT`

And replacing with:

• `n = m/M`, where M is molar mass

• `rho = m/V`

• `implies n = (rho V)/M`

Leads to:

`PV= (rho V)/M RT, qquad P = (rho RT)/M`

So:

`square implies c = sqrt((gamma RT)/M)`

An expression that references the temperature of the fluid.