How does Sound pressure Level vary with air pressure?

Question

If a sound source is placed 1 meter away from a decibel meter reading X decibels at ambient pressure, what would that decibel meter read at the same distance at 500 hPa of pressure, or really any pressure P? Everything else is kept constant. Is there a formula to determine this? Since there is no sound reading at a complete vacuum, would it decrease linearly? I have searched a lot but found no answer, this is my last resort. Thanks in advance for any answer

Answer 1

It depends on the sound source. Obviously, if you hit a drum in vacuum, there will not be any sound emitted even if you hit the drum with the same impact.

If you somehow manage to build a sound source that emits the same acoustic power (watts) at 1013 hPa and at 500 hPa, and your dB meter is designed to work properly across that pressure range as well, then the dB meter will give the same number.

Usually, sound in air is emitted from a moving surface. If the surface movement (frequency and amplitude) is the same whether there is air around or not , then the air adjacent to the surface will be compressed and expanded by a fixed factor. In that case, the sound pressure level (as a pressure amplitude in Pa) will be proportional to the ambient pressure; a factor 2 in pressure will be equivalent to 6 dB.

For devices that are designed to emit sound, such as musical instruments and loudspeakers, it is more complicated. At a reduced counterpressure from the ambient air, the amplitude of the emitting surface will likely increase. In the extreme case of an idealized drum open drum, with a drum skin that is perfectly elastic, mounted to a perfectly rigid frame, the only way the energy placed in the stretching of the skin can be dissipated is by emitting sound. In that case, you'd expect 0 dB change in acoustic output - as long as exactly the same amount of energy is placed into the drum skin.

But if you excite the drum skin by an impact of a drumstick given mass and a given velocity, the amount of energy that will be transferred to the drum skin will depend on whether there is counterpressure from the ambient air (or an enclosed space behind the skin). The drumstick may bounce nearly elastically (no net energy transfer) or inelastically (large net energy transfer), depending on the mass of the drumstick, where it hits the skin, and so on. The change in SPL could be positive or negative for a small change in ambient pressure.

Loudspeakers are generally designed with the ambient air pressure in mind. Their sensitivity is affected a bit by the ambient pressure, but it depends on the frequency and loudspeaker design how much and in what direction. Someone tried this with loudspeakers at sea level and at altitude, but they scaled the measurements to be equal at 1 kHz.