## 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

## Understanding Decibels & Why OSHA Pays Attention to Your Noise Exposure

In the simplest of metric terms, a decibel is one-tenth of a bel.  But, historically, bel was a unit created to honor Alexander Graham Bell who invented the telephone.  In the early days with telephone wires, they noticed that the signal strength would decay over a long distance.  In order to determine power requirements to connect people for communications, they determined that they could use the ratio of power levels.  As a start, it had to be based on a minimum amount of power required for a person to hear on the telephone.  They found that the signal power level to generate an angular frequency of 5000 radians per second would be that minimum value as determined by an average number of people.  They used this mark as a reference point in the ratio of power levels.  Because of the large variations in values, they simplified the equation on a base-10 log scale and dividing the bel unit by 10.  Thus, creating the measurement of decibel.

Today, this same method is used to measure sound.  Like frequency waves that travel through the telephone wires, pressure waves travel through the air as sound.  This sound pressure is what our ears can detect as loudness, and it has a pressure unit of Pascals (Pa).  As an example, a small sound pressure would be like a whisper while a large sound pressure would be like a jet engine.  This is very important to know as high sound pressures, or loudness, can permanently damage our ears.

With sound pressures, we can determine the Sound Pressure Level (SPL) which is measured in decibels (dB).  Similar to the equation for the telephone power signals above, the SPL also uses a ratio of sound pressures in a base-10 logarithmic scale.  For a minimum reference point, an average human can just start to hear a sound pressure at 0.00002 Pa.  So, the equation for measuring sound levels will use this minimum reference point as shown in Equation 1.

Equation 1:

L = 20 * Log10 (p/pref)

where:

L – Sound Pressure Level, dB

p – Sound pressure, Pa

pref – reference sound pressure, 0.00002 Pa

Why is this important to know the decibels?  OSHA created a chart in 29CFR-1910.95(a) that shows the different noise levels with exposure times.  This chart was created to protect the operators from hearing loss in work environments.  If the noise level exceeds the limit, then the operators will have to wear Personal Protection Equipment (PPE), or suffer hearing damage.  EXAIR offers a Sound Level Meter, model 9104, to measure sound levels in decibels.  It comes calibrated to accurately measure the sound to determine if you have a safe work environment.

There is a term that is used when it comes to loud noises, NIHL.  This stands for Noise Induced Hearing Loss.  Once hearing is damaged, it will not come back.  To keep your operators safe and reduce NIHL, EXAIR offers many different types of blow-off products that are designed to decrease noise to a safe level.  So, here’s to Alexander Graham Bell for creating the telephone which can be used to contact EXAIR if you have any questions.

John Ball
Application Engineer
Email: johnball@exair.com

Photo of Telephone by Alexas_FotosCC0 Create Commons

## Super Air Knife Math – When 72 + 72 = 75

The Super Air Knife is the latest generation of EXAIR engineered air knife that dramatically reduces compressed air usage and noise when compared to other blowoffs.

From the chart above, the Super Air Knife when supplied with 100 PSIG of compressed air has a sound level of just 72 dBA (A-weighted decibel scale) when measured from 3′ away.  72 dBA is a moderate sound level, and some common comparisons are ‘normal speaking voice’ at 70 dBA and ‘living room music’ at 76 dBA.

For many processes, such as a bottling line drying operation, a pair of the air knives delivers the best performance. When asked, “what is the sound level for (2) of the knives,” a little Acoustic Engineering is in order. Because the decibel scale is logarithmic, the result is not as simple as adding 72 + 72 = 144.  144 dBA is in the range of a jet aircraft take off! Thankfully, both the actual sound level and the numerical value are determined another way.  I’ll spare you a lot of the math but the equation is as below.

… where SL1, SL2, SL3 are the sound levels in dBA of the each sound makers, for as many that are being combined.

In the case of (2) Super Air Knives operated 100 PSIG, the combined sound works out to be a quiet 75.0 dBA — a powerful, efficient and quiet product ideal for many applications and process within the manufacturing environment.

As a helpful rule of thumb- combining any (2) items will yield an increase of 3 dBA, combining (3) results in a rise of 4.8 dBA, and combining (4) results in a 6 dBA rise over just (1) of the items.

The Super Air Knives have been successfully used in a wide range of applications, including part drying, sheet and conveyor cleaning, web cooling, scrap removal, pre-paint dust blowoff, and many, many more.

To discuss your application and how an EXAIR Intelligent Compressed Air Product can make your process better and quieter, feel free to contact EXAIR and myself or one of our other Application Engineers can help you determine the best solution.

Brian Bergmann
Application Engineer

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