Question

Why the speed of sound in air not depend upon pressure?

Answer 1

Beause sound is moved in a vaccum .And pressure is equals to speed upon time.So sound does travel in a vaccum

Answer 2

The speed of sound in an ideal gas, cideal, is given by

cideal=γ⋅pρ−−−−√

where

γ is a parameter known as the “adiabatic index.” For monatomic gases, γ=1.666, while for diatomic gases, γ=1.400

p is the pressure

ρ is the density

If we compress an ideal gas, the pressure goes up, but the density goes up by exactly the same factor. Hence the speed of sound in an ideal gas is independent of pressure.

We can plug in real numbers to see how closely the above equation matches real gases:

At IUPAC standard temperature and pressure (0 °C and 100 kPa) dry air has a density of 1.2754kg/m3. (Wikipedia has contradictory figures.) Air consists mostly of diatomic molecules, O2 and N2. Since 1 Pa=1 kgm⋅s2,

cair≈1.400⋅1000001.2754−−−−−−−−−−√≈331.3m/s, which is close to published values.

Since, for an ideal gas, pV=nRT, we can also write

cideal=γ⋅R⋅TM−−−−√

where

R is the gas constant

T is the absolute temperature

M is the molar mass

So the speed of sound goes up with higher temperature, and goes down with increasing molar mass.