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Audio Technica

# The Scoop On SPL: Getting A Handle On Decibels And Distance

## Looking at the way sound pressure levels (SPL) drop in decibels (dB) depending on the listener's distance from the sound source.

By Mike Sokol December 12, 2018

This is a basic primer on sound levels and how they work, especially when a sound system is outdoors. It’s not an exhaustive study on acoustics or how much sound level is dangerous. Rather, we’re going to explore how sound pressure levels (SPL) drop in decibels (dB) depending on the listener’s distance from the sound source.

We’ve all been there when playing or running sound for a band outside, or maybe even doing a few DJ gigs for an outside wedding party. There are a few houses down the street complaining about the loudness of the music. Or maybe there’s a noise ordinance stating no more than XX dB after XX pm. Here’s how to get a handle on what all of this decibel brouhaha is about.

## The Backstory

Who is this SPL you speak of, and what’s a dB? Glad you asked. A dB is a decibel, which is a combination of the terms deci and Bel. The deci means 1/10th, as in decimal place, or like a dime is 1/10th of a dollar. So a decibel is 1/10th of a Bel.

But what is a Bel? It’s a ratio of power measurement named for the famous inventor Alexander Graham Bell, the father of the telephone. We typically use the term dB (decibel) for most measurements since that gives us a much more usable number than a Bel, which is huge.

Technically, dB SPL is a unit used to express the relative pressure of a sound wave, equal to 20 times the common logarithm of the ratio of the pressure produced by the sound wave to a reference pressure, usually 0.0002 microbar (more on that a bit later).

I won’t bore you with all of the calculations but know that a decibel (dB) is simply a ratio of power, and that +3 dB equals a doubling of power, +6 dB equals 4 times the power, and +10 dB equals 10 times the power. Subtracting decibels by using a minus sign works the same way: -3 dB is 1/2 the power, -6 dB is 1/4 of the power, and -10 dB is 1/10 of the power.

Figure 1 makes the dB relationship clear. This is called a logarithmic relationship, just like the Richter Scale, the numerical scale for expressing the magnitude of an earthquake. And log ratios are handy since they make it easy to compare power levels with simple addition and subtraction.

Figure 1: The dB for power relationship.

But before we get to that, we have to define SPL, which again, stands for sound pressure level. We often see the term SPL combined with dB for loudspeaker ratings, as in 110 dB SPL at 1 meter. Many times you might see just: “110 dB” but that’s nonsensical because 110 dB is a ratio without any reference level to compare against.

SPL does indeed have a reference level which is 20 micro-pascals of sound pressure. So 0 dB SPL is 20 micro-pascals of modulation of the atmospheric pressure, which is the quietest sound that a human can hear under perfect conditions.

Pressure in acoustics is like voltage in electronics in that it has a squared relationship to power, so the calculation becomes 20 log (ratio). This means that +6 dB SPL would be 2 times the pressure, +12 dB SPL would be 4 times the pressure, +20 dB SPL would be 10 times, +40 dB SPL would be 100 times, +60 dB would be 1,000 times and +80 dB SPL would be 10,000 times. And yes, 120 dB SPL would be 1,000,000 times the pressure of 0 dB SPL.

Now, it doesn’t “sound” 1 million times louder (thankfully) since our own hearing is also logarithmic. That is, every time we add 3 dB of power the sound level gets just noticeably louder, and every 10 dB makes it sound about twice as loud. If we’re comparing two loudspeakers, one playing at 90 dB SPL versus another one that’s playing at 100 dB SPL, the 100 dB one sounds twice as loud to our ears but it’s really putting out 10 times as much acoustic power.

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Mike Sokol

System Designer & Audio Educator
Mike Sokol does sound system design and training for JMS Productions, his consulting company in Western Maryland. Visit www.livesoundadvice.com for his educational articles and videos, and email him at [email protected] with comments and suggestions.

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##### Conor Mullan says

Wasn't Alexander Graham Bell from Scotland?
I suppose Andy Murray is America's 2nd greatest tennis player at the moment?
;-)

##### Conor says

Alexander Graham Bell was Scottish not American.

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