## 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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## Sound Levels in Your Facility

One of the most common and dangerous hazards that occur within a manufacturing and production facility is the noise level within the plant. Noise is measured in units known as decibels. Decibels are a ratio of the power level of the sound compared to a logarithmic scale. If an employee is an exposed for too long to high levels of noise, they can begin to lose their hearing. That is where the OSHA 29 CFR 1910.95 regulation comes into play.

This OSHA standard doesn’t just provide the protection against noise in the work place but monitoring as well. Companies shall provide at no cost audiometric tests for all employees to ensure that no damage is being to the hearing of all personnel. This program is to be repeated every six months and the results are to be made accessible to all personnel.

Hearing is very important to our everyday lives and must be protected due to the fact that once it is damaged hearing loss cannot be lost be repaired. The OHSA 29 CFR 1910.95 is there to protect and monitor this dangerous hazard in the workplace so that all employees can go home safe and sound.

Here at EXAIR we design all of our products to safe and quite. Weather it is using one of our mufflers for vortex tubes or E-vac’s or one of our Super air nozzles we strive to meet and exceed the OSHA standard. One could also purchase EXAIR’s Digital Sound Level Meter which can give a accurate and responsive reading of how loud your compressed air sources are.

For more information on EXAIR’s Digital Sound Level Meter and any of EXAIR‘s Intelligent Compressed Air® Product lines, feel free to contact EXAIR and myself or any of our Application Engineers can help you determine the best solution.

Jordan Shouse
Application Engineer

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## Silencing Mufflers

I live near an amusement park called Kings Island. In the later part of Spring I can hear and see the people and rides. As the Summer enters and the tree leaves have all grown they act like a muffler reducing the roller coaster noises and screaming people on the roller coasters. These trees are not high enough to block the nightly fireworks but this is a good thing for me as I enjoy the sights and sounds of the fireworks.

An important focus in every manufacturing environment is a “Noise Reduction” campaign making a safer and healthier area for people working in the environment. EXAIR has Silencing Mufflers that can support your efforts for noise reduction. We have a variety of mufflers which will help to reduce work area noise produced by air exhausting from cylinders, valves and other air powered equipment. EXAIR Silencing Mufflers help plants meet OSHA Standard 1910.95(a) by reducing the sound to safer levels. Not only do our Silencing Mufflers reduce sound but they also eliminate harmful dead end pressures by covering up an open port or opening. These openings do not have a pathway for harmful pressurized air to escape if they become blocked.

Sintered Bronze Mufflers: A low cost solution and easy to install in new and existing air powered products. Sintered bronze muffler come in a variety of sizes (10-32 thread size up through 1/2-20 UNF female) and are capable of passing a certain volume of air with minimal back pressure restriction.

Reclassifying Mufflers: These mufflers are an upgrade from Sintered Bronze Mufflers. They offer the best noise reduction, up to 35 decibels. Available from 1/8 NPT up to 1 NPT. Reclassifying Muffles also eliminate oil mist. The patented wrap design of the removable element separates oil from the exhausted air so virtually no oil is released into the environment.

Straight-Through Mufflers: These mufflers offer a corrosion resistant aluminum outer shell lined with sound absorbing foam for better noise reduction. The typical noise reduction is up to 20dB.

Heavy Duty Mufflers: feature a corrosion-resistant aluminum outer shell with an internal stainless steel screen that protects valves and cylinders from contamination that could enter through the exhaust ports. The typical noise reduction is up to 14 dB.

EXAIR can help in your noise reduction projects with many options to consider. If you have any questions or need help selecting the right muffler for your needs please contact any of our qualified Application Engineers.

Eric Kuhnash
Application Engineer
E-mail: EricKuhnash@exair.com