The Trick To Adding Sound Levels Of Multiple Sources

If I put a 10 pound weight on a scale, the scale will read 10 pounds. If I put another 10 pound weight next to it, the scale with now read 20 pounds.

If I have $10 bill in my pocket…well, that’s a LOT more cash than I usually carry. But if I somehow come into possession of another $10 bill and put it in my pocket, now I have $20. And it probably won’t be for long.

If there’s an EXAIR Model 1100 Super Air Nozzle supplied with compressed air at 80psig, and my Sound Level Meter is reading a level of 74 dBA, and I hook another one up right next to it, my Sound Level Meter now reads about 78 dBA.

Wait, what? Did we just break math there? You, and your ears, will be happy to know that there’s perfectly valid math behind the third (as well as the first two) statements above. The third one’s just a little different, that’s all.

See, sound power (that’s “how loud” sound is, as measured at the point of generation) and sound pressure (“how loud” it is, as measured at the point where it’s heard) are both quantified in units called decibels. And, unlike mass or wealth (the first two examples above), which are linear & additive, measurement of sound power & pressure is done on a logarithmic scale. That means simple arithmetic won’t work…we have to use a logarithmic equation to ‘add’ those sound levels together. It looks like this:

Combined Sound Level (dBA) = 10 x log10[10SL1/10 + 10SL2/10 + 10SL3/10 …]

Where “SL1”, “SL2”, “SL3”, etc., are the sound levels, in decibels, for the “noisemakers” in question. So, for the two Model 1100 Super Air Nozzles, generating 74 dBA each:

10 x log10[1074/10 + 1074/10] = 77.65 dBA

And just to prove the math works, we made a video of a real live test:

All EXAIR Intelligent Compressed Air Products are engineered & manufactured to be safe, efficient, and as quiet as possible. If you’d like to find out more, give me a call.

Russ Bowman, CCASS

Application Engineer
EXAIR Corporation
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Measuring And Adding Sound Levels Together

What sound level do you get when you feed an EXAIR Super Air Nozzle at 80psig? What if there are two of them?  Or three?  Grab your scientific calculators, folks…we’re gonna ‘math’ today!

But first, a little explanation of sound power & sound pressure:

Strictly speaking, power is defined as energy per unit time, and is used to measure energy generation or consumption.  In acoustics, though, sound power is applicable to the generation of the sound…how much sound is being MADE by a noisy operation.

Sound pressure is the way acoustics professionals quantify the intensity of the sound power at the target.  For the purposes of most noise reduction discussions, the target is “your ears.”

The sound levels that we publish are measured at a distance of 3 feet from the product, to the side.  The units we use are decibels, corrected for “A” weighting (which accounts for how the human ear perceives the intensity of the sound, which varies for different frequencies,) or dBA.  Also, decibels follow a logarithmic scale, which means two important things:

  • A few decibels’ worth of change result in a “twice as loud” perception to your ears.
  • Adding sources of sound doesn’t double the decibel level.

If you want to know how the sound level from a single source is calculated, those calculations are found here.  For the purposes of this blog, though, we’re going to assume a user wants to know what the resultant sound level is going to be if they add a sound generating device to their current (known) situation.

Combined Sound Level (dBA) = 10 x log10[10SL1/10 + 10SL2/10 + 10SL3/10 …]

Let’s use an EXAIR Model 1100 Super Air Nozzle (rated at 74dBA) as an example, and let’s say we have one in operation, and want to add another.  What will be the increase in dBA?

10 x log10[1074/10 + 1074/10] = 77.65 dBA

Now, there are two reasons I picked the Model 1100 as an example:

  • It’s one of our most versatile products, with a wide range of applications, and a proven track record of efficiency, safety, and sound level reduction.
  • We proved out the math in a real live experiment:

Why do I care about all of this?  My Dad experienced dramatic hearing loss from industrial exposure at a relatively young age…he got his first hearing aids in his early 40’s…so I saw, literally up close and very personal, what a quality of life issue that can be.  The fact that I get to use my technical aptitude to help others lower industrial noise exposure is more than just making a living.  It’s something I’m passionate about.  If you want to talk about sound level reduction in regard to your use of compressed air, talk to me.  Please.

Russ Bowman
Application Engineer
EXAIR Corporation
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