40 Pressure amplitude

Pressure differences and human hearing

The human brain forms an impression of loudness based on the properties of the vibrations that enter the ear. You might figure that amplitude of the vibration at the eardrum is the dominant factor for our perception of loudness, and you’d be basically correct. Our brains generally associate bigger vibrations with “louder” sounds.

Human ears work by detecting the tiny pressure difference between compressions and rarefactions in a sound wave. The size of these pressure variations is called pressure amplitude. In general, the larger the pressure amplitude a sound has, the louder it seems. These pressure changes are tiny compared to atmospheric pressure, even for extremely loud sounds. Sounds loud enough to damage human ears (e.g. a jet plane at 30 yards) have pressure variations of just a few hundred Pascals- that’s less than one hundredth of atmospheric pressure (which is roughly 100,000 Pa). The quietest sounds humans can detect have pressure amplitudes of about – roughly one billionth of atmospheric pressure.

Pressure amplitudes in sound are small (compared to atmospheric pressure), but they span an incredibly wide range- sounds loud enough to damage the ear have pressure amplitudes roughly a million times larger than the quietest sounds we can hear! See the table later in this section to see the incredibly wide range of pressure amplitudes involved in everyday sounds.

This wide dynamic range is generally a “good thing”- it’s why we can hear both mosquitoes and jet planes. However, there is at least one drawback: we have difficulty noticing differences in amplitudes- two jet planes simply don’t sound that much louder than one.

Sound pressure: a confusing phrase

Authors often use the words sound pressure when they actually mean pressure amplitude. Because so many books (including this one!) use this horrible phrase, you should be aware of the term and its usual meaning: sound pressure means pressure amplitude.

Don’t confuse sound pressure with air pressure- they are not the same thing! The phrase “sound pressure of 1 Pa” seems like it describes a sound that has air pressure with a steady value of 1 Pa- nothing could be further from the truth! The air pressure in the room with that sound is neither steady, nor anywhere near 1 Pa.  The average air pressure in any sound wave (in air) is typically close to 101,300 Pa (i.e. atmospheric pressure). What “sound pressure of 1 Pa” means is that the air pressure in the sound wave varies, but remains within 1 Pa of atmospheric pressure.

Sound Pressure Level

Sound level meters generally work by measuring pressure amplitude (aka sound pressure) with a microphone. Because the numbers for sound pressure span such a wide range, sound level meters display sound pressure level (SPL), instead of sound pressure (aka pressure amplitude). Sound pressure level is a number based directly on pressure amplitude, expressed in decibels (dB). The table below compares sound pressures and sound pressure levels for some everyday sounds.

The decibel scale basically transforms sound pressure numbers into a much more human-friendly format using the math of logarithms.