What's the loudest possible sound?

posted Jan 18, 2015, 11:59 AM by Patrick Poole   [ updated Jan 18, 2015, 11:59 AM ]
Nice ear shot
The human sense of hearing is quite remarkable—you’re able to perceive things from a quiet whisper up to a rock concert effortlessly. You’ve probably heard that prolonged exposure to concerts can be bad for your hearing, as can standing nearby a jet taking off. Today I’ll discuss a bit of what goes into measuring sounds and how your brain interprets loudness, and also tell you just how loud a sound can possible be.

Sound waves are traveling air compressions induced by the motion of some physical object

We’ve discussed before how sound waves are really air compressions traveling away from some source. Physical motion like a hand clap will push air out of the way somewhere, creating a denser region of air just nearby. That denser region only exists for a moment before the air molecules move to fill the less dense region nearby, and then that dense region will also move to fill the adjacent sparse region, and so on.

In this way a compression wave will travel away from some source, getting weaker as it goes because that compression is being spread out into more area. The sphere of compression is getting larger as it travels, but the source only had a finite amount of energy—so the sound gets weaker as it travels because the energy is spread over a larger area, and weaker compression waves mean the sound is more difficult to hear.

Louder sounds spread more air
Compressions (denser regions of air) and expansions (sparser regions) make up the traveling wave, and the difference between these densities is related to the loudness

Clapping softly and forcefully will both feel and sound different. When you clap hard, you’re pushing air out from between your hands more quickly, which knocks them into their neighboring air molecules more forcefully. The impact you feel is related to how quickly that air gets shoved.

The traveling sounds wave that emanates from your hands moves outward as compressions, or regions of greater than normal air density, and rarefactions, or region of lower than normal air density. You can see the same sort of wave travel if you hang a slinky from your hand and move your hand up and down—bits of the spring will expand and contract, so you could say there is more slinky density at some points and less at others as the wave travels.

Slinky sound
The power of a sound is measured in decibels, but its loudness also depends on how your brain interprets it

It’s important for scientist to use specific language when describing things, and to be explicit about the pieces involved in that explanation. For example, there are ways of characterizing the strength of a sound: you can describe the energy carried within the sound wave, and from that the power (which is energy per time) or intensity (which is energy per time per area) of the sound—all of which are different things.

None of those quantities, however, are exactly the same as loudness. How loud a sound seems is certainly related to how much energy or power is carried by the wave, but it also depends on how that sound affects your ear drum, and then how your brain interprets that signal into the perception of sound. It turns out your brain averages the last second or so of ear drum vibrations when it interprets a sound—in this way, the same energy sound wave will seem louder to you if that energy is spread out into a longer bit of time, as long as that time is less than one second.

Sound chart

The power carried in a sound wave is often described in units called decibels. Decibels can be a bit confusing because they are a logarithmic scale of measurement—this means that an increase of 10 decibels means the sound is 10 times as powerful, and an increase of 20 decibels means the sound is 100 times as powerful as before. Other logarithmic scales are the chemical pH scale, and the Richter scale for measuring earthquake strength. A 8.0 earthquake is really ten times(!) as strong as a 7.0, because the scale is logarithmic. Importantly, to use decibels you also need a reference point. For sound in air this is typically chosen to be 20 micropascals of air pressure, which is about the lower threshold for human hearing.

With that being said, human sound perception is also logarithmic—now I’m talking about how your brain interprets the loudness. To you, a 50 decibel indoor conversation will only seem twice as loud as a 40 decibel library, even though the actual sound power is ten times as great. This logarithmic sense of sound allows you to interpret noises over a much larger range, so you can quickly adjust from 20 decibel rustling leaves to 100 decibel jackhammers.

Even though I’ve titled this post “what’s the loudest sound”, I’m going to ignore the effects from human interpretation of a sound wave, and focus instead on the physics of the waves themselves. I really should have called the post “What’s the most powerful sound possible?”, but that doesn’t have the same ring to it.

The loudest possible sound (at sea level in air) is 194 dB, when a full rarefaction (vacuum pocket) occurs

Imagine you’re doing the slinky experiment again, but now you hold the slinky in both hands and pull apart quickly. If you do this hard enough you’ll break the slinky somewhere in the rarefied (or sparse) region, because there the wave motion is pulling apart the spring more than it can handle.

This same thing can happen in the air: at some point a strong sound wave will have no air molecules within its rarefaction area—they all went to one side into the compression zone, and left a small pocket of vacuum. A moment later the surrounding air will rush back in, and do so strongly enough that another vacuum pocket is formed where there was just a compressed region—in this way the strong sound wave propagates, but it couldn’t be any stronger because there isn’t any more air to displace from the rarefaction zone.

Slinky breaking wave

You can see how this will be different depending in the density of the air, and on the air pressure (pressurized air will resist being displaced more than normal pressure air). For sea-level pressure and temperature air (STP, or standard temperature and pressure, and with the standard reference of 20 micropascals of pressure) the intensity of a sound wave that has rarefaction regions with no air molecules in them is 194 decibels. At higher altitudes this value will be lower, since there is less air to move. Underwater where the density and pressure is much higher, this most intense sound is also much higher—a whopping 256 decibels.

For perspective remember what we said about logarithmic decibel scales: this is about 60 decibels higher than the loudest sound possible in air, which means to you it would sound 26 = 64 times as loud, and its power is 106 = 1,000,000 times larger! That’s as big of a difference as there is between an air conditioning unit and a thunderclap.

Bonus physics—Most intense laser
Plasma ball in air

There is a maximum amount of sound energy that can travel through the air, and the same is true for light energy as well. This will only happen for very intense levels of light, light those from modern lasers. If an intense laser is focused tightly enough, it’s possible to rip electrons from their atoms in the air itself and cause a small plasma streak to form, like in the image to the right—this effect is similar to lightning, but it is stationary because it will only happen where the laser intensity is high enough.

Even in vacuum with no air atoms to pull electrons from, there is still a maximum light intensity. Above an incredibly large intensity called the Schwinger limit, the light is strong enough to create a positron-electron pair out of the vacuum itself. Current lasers are nowhere near this intensity level, but scientists are working to reach this point one day in the future. I’ll leave the details to a future post.