# What is the relation of sound propagation to air pressure?

I am wondering, air makes sound propagate. So in a vacuum there is no sound, but what is the relation of pressure to sound volume? Is it linear?

If I have a source of sound and let's say I am in a room with an air pressure half of the pressure outside, would the sound be 0.5 lighter? Or does air pressure have no impact on the sound volume?

Is there a comprehensible formula for that?

• Your title is confusing, since you're asking about sound volume in the body and people might interpret the title as asking about sound speed... – j.c. Nov 12 '10 at 21:54

The sound intensity is

$I = \xi^2 \omega^2 c \rho$

where $\xi$ is the particle displacement, $\omega$ the frequency, $c$ the speed of sound and $\rho$ the density of the medium.

What does this mean?

You're in a room where the pressure is lower (and so the density of air is also lower). Say that your sound source (string, speaker or whatever) is vibrating with the same amplitude and frequency, so $\xi$ and $\omega$ don't change. The speed of sound is roughly independent of the pressure. So your sound intensity will be roughly proportional to the density of the air, or proportional to the pressure.

• density of medium would be measured here in mbar ? – Artur Ejsmont Nov 13 '10 at 19:03
• All units are SI (see the link). So the density is measured in kg/m^3. Mbar is a unit of pressure. – dF_ Nov 13 '10 at 19:22
• Of course, if temperature changes, the pressure could change without the density changing. – David Z Dec 21 '10 at 7:57

Propagation speed in an ideal gas varies as the square root of pressure. It also depends on the adiabatic index, the density of the gas, and the temperature of the gas.

• Speed of sound $c =\sqrt{\frac{\gamma p}{\rho}} = \sqrt{\gamma R T}$. So the speed of sound is independent of pressure because if the pressure decreases so does the density at the same rate. – Farcher Nov 23 '16 at 18:37

The volume of sound is measured in decibel (dB), which are a measure of air pressure.

Sound pressure level (SPL) or sound level Lp is a logarithmic measure of the effective sound pressure of a sound relative to a reference value. It is measured in decibels (dB) above a standard reference level.

http://en.wikipedia.org/wiki/Sound_pressure#Sound_pressure_level

A undistorted sound cannot be carried by more pressure than it's available. In other words, at 1 atm, a sound can only reach 191dB, which correspond to 1 atm.

Over that, we are basically talking about shockwaves.

• How would the sound pressure level of the same clap at 1/2 atm versus 1 atm compare? I think that's the question being asked here. – j.c. Nov 12 '10 at 21:53