## Sound Pressure, Sound Power, and Sound Intensity Explained

We are all familiar with sounds in everyday life.  Some sounds are pleasant, and some sounds can be destructive.   Sound has exponents of pressure, power, and intensity.  In this blog, I will go over each one to see how we perceive sound and are affected by it.

Sound pressure is what our ears pick up.  The small bones in our ears detect pressure changes with our eardrums to convert to noise signals.  In looking at a single source, sound pressure is created by sound waves. .  In looking at a single source, sound pressure is created by sound waves.  The units are measured in Pascals.  The lowest pressure perceived by human ears is 0.00002 Pa, and we can use this value as a reference point.  Depending on the frequency, pain can occur at 65 Pa.  We can arrive at a sound pressure level which is measured in decibels, dB.  This correlation between sound pressures and sound pressure levels is calculated by Equation 1.

Equation 1:

L = 20 * Log10 (P / Pref)

L – Sound Pressure Level, dB

P – Sound pressure, Pa

Pref – reference sound pressure, 0.00002 Pa

Sound pressure has to be measured at a certain distance.  Like a wave in a pond, the farther the distance, the smaller the waves.  Most standards are set at 1 meter away.  As an example, the sound pressure from a passenger car as heard from the roadside is 0.1 Pa.  With Equation 1, we can get the following decibel level:

L = 20 * Log10 (0.1Pa / 0.00002Pa) = 74 dB

Sound power deals with the amount of energy that is generated at the source, which is independent of distance.  There is an old saying, “if a tree falls in the forest and no one is nearby, does it make a sound?”.  Well, it does.  Even though you may be too far away from the source to detect the sound pressure waves, it still creates a sound.  Sound power is important to measure noise in different locations around the source.  This will help to ensure proper protection for the workers in the different areas.  The unit of measure for sound power is watts (W).  Equation 2 shows the formula to calculate sound power levels.  This equation also uses a reference point which was determined by a standard to be 1 pW or 1 * 10-12 Watts.

Equation 2:

LN = 10 * Log10 (p / pref)

LN – Sound Power Level, dB

p – Sound power, W

pref – reference sound power, 1 * 10-12 W

As an example, a jet engine can generate roughly 1 watt of sound power.  From Equation 2, we get a sound power level of

L = 10 * Log10 (1 W / 1 * 10-12 W) = 120 dB

To avoid confusion with sound pressure levels, we usually use the unit of bel (B) rather than decibel (dB).  So, the jet engine would produce a sound power level of 12 Bel.

Sound intensity is defined as sound power per unit area; it is commonly measured in Watts per square meter, W/m2.  The formula is shown in Equation 3.

Equation 3:

I = p / A

I – Sound Intensity W/m2

p – Source power, W

A – Area from source, m2

From the sound source, the sound intensity is developed by the direction the sound “flows” through a particular area.  If you have ever seen a band trying to setup their sound system, they take into account walls, the size of the room, open areas, speaker angles, etc., to enhance the sound.  The sound pressure, or loudness, will travel through a median at a distance, which could encounter walls, machines, ceilings, etc.  Let’s look at the sound power of the jet engine above at 1 Watt.  If a plane was flying 1,000 meters (3,300 feet) above your head, you could find the sound intensity.  First, sound travels in all directions; so, we will use the surface area of a sphere, 4πr2 to calculate the area.  Since the source is at the center, the distance to the person will be the radius.  So, at 1,000 meters, the area will be 4 * 3.14 * (1,000 m)2 = 12,560,000 m2.  We can deduce from Equation 3 that

I = p / A = 1 W / 12,560,000 m2 = 7.96 * 10-8 W/m2

To correlate this to the sound intensity level, which your ears perceive, it is measured in decibels, dB, and is represented by Equation 4.

Equation 4:

Li = 10 * Log10 (I / Iref)

Li – Sound Power Intensity, dB

I – Sound intensity, W/m2

Iref – reference sound intensity, 1 * 10-12 W/m2

With the example above of the jet engine that is 1,000 meters above our head, we can calculate the sound level that our ears can hear.  From Equation 4, we have

Li = 10 * Log10 (7.96 * 10-8 W/m2 / 1 * 10-12 W/m2) = 49 dB

Hearing loss is permanent; and it is the most recorded occupational illness in manufacturing plants.  The Occupational Safety and Health Administration (OSHA) is the enforcement agency responsible for determining and fining companies that violate this directive; 29 CFR 1910.95(a).  To keep your operators safe, it is important to measure the sound level of your pneumatic equipment.  NIOSH, or the National Institute for Occupational Safety and Health, uses a Hierarchy of Controls for dealing with safety issues.  And the Engineering Controls is more prevalent on this chart than purchasing personal protective equipment or PPE (reference diagram above).  EXAIR manufactures these engineered products for safety, noise reduction, and cost savings.  They are known as the Intelligent Compressed Air Products®.  To minimize any hearing loss with personnel, EXAIR has a variety of Super Air Nozzles, Safety Air Guns, Super Air Amplifiers, and Super Air Knives that can reduce the sound levels to a safe level.  And as a bonus, it will save you money by reducing your compressed air usage.  You can talk with one of our Application Engineers if you wish to reduce the surrounding sound levels with your pneumatic blow-offs.

John Ball
Application Engineer
Email: johnball@exair.com

## 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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## Understanding Noise: Sound Power Vs. Sound Pressure

Sound Power and Sound Pressure have been covered a few other times here on the EXAIR Blog. Once here by Brian who made the visual correlation in regards to a speaker and a musical instrument. And here by Russ who breaks down how you calculate sound power level with the below equation! All machines generate sound when they are in operation. The propagated sound waves cause small changes in the ambient air pressure while traveling. A sound source produces sound power and this generates a sound pressure fluctuation in the air. Sound power is the cause of this, whereas sound pressure is the effect. To put it more simply, what we hear is sound pressure, but this sound pressure is caused by the sound power of the emitting sound source. To make a comparison, imagine for example a simple light bulb. The bulb’s power wattage (in W) represents the sound power, whereas the bulb’s light intensity represents the sound pressure. Sound power does not generally depend on the environment. On the contrary, the sound pressure depends on the distance from the source and also on the acoustic environment where the sound wave is produced. In the case of indoor installations for example, sound pressure depends on the size of the room and on the sound absorption capacity of the surfaces. For instance, say the room walls don’t absorb all the sound but reflect parts of it, then the sound pressure will increase due to the so called reverberation effect. (reverberation time is broadly defined as the time it takes for the sound pressure to reduce by 60 dB after the sound emitting source has been shut off). OSHA puts the following limits on personnel exposure to certain noise levels: EXAIR’s line of Intelligent Compressed Air Products are engineered, designed, and manufactured with efficiency, safety, and noise reduction in mind.  If you’d like to talk about how we can help protect you and your folks’ hearing, call us. Jordan Shouse Application Engineer Send me an email Find us on the Web  Like us on Facebook Twitter: @EXAIR_JS Light Bulb image courtesy of  josh LightWork  Creative Commons License

## 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
Visit us on the Web