## 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
Twitter: @EXAIR_jb

## What is Sound: The Correlation Between Sound Power and Sound Pressure

Sound, it is all around at every given point of the day. Whether it is from the music we listen to, the person talking to you, your cars engine, or the wind blowing through the leaves there is no escaping it. Hearing is one of the five senses that the majority of humans rely on and should be protected at all costs and with a good understanding of what sound is, one can help mitigate damage done to their hearing. Sound can be broken down into two parts, sound power and sound pressure. But the real question is, how do these corollate to each other to become the sound that we rely on.

Sound Power (Watts) is defined as the rate at which sound energy (decibels) is emitted, reflected, transmitted or received, per unit of time. Whereas, Sound Pressure is defined as the local pressure deviation from the ambient atmospheric pressure, caused by a sound wave. Based on these two definitions it can be determined that sound power is the cause that generates the sound wave and sound pressure is the effect or what we hear after the sound wave has traveled to the ear.

This can be summed up in a simple analogy using a light bulb. Light bulbs use electricity to generate a source of light, this means that the power required (also stated in Watts) to cause the bulb to light up is comparable to Sound Power. The intensity of the light being generated (stated in Lumens) would be the Sound Pressure. Sound Pressure is what we would typically hear or call sound. This is what is measured because that is the harmful aspect to our hearing and ears. If the Sound Pressure is high enough and the ear is exposed to it long enough, permanent damage can be done resulting in hearing loss to the point of complete hearing lose.

I have known many people who have lost there hearing either completely or a large portion of it from exposure to loud noises. EXAIR designs and manufactures quiet and efficient point of use compressed air products. These products either meet or exceed the OSHA noise Standards in OSHA Standard 29 CFR – 1910.95 (a).

If you are not sure what the noise level is in your facility check out EXAIR’s Digital Sound Level Meter. It’s an easy to use instrument for measuring Sound Pressure levels in an area.

If you have questions about the Digital Sound Level Meter, or would like to talk about any of the quiet EXAIR Intelligent Compressed Air® Products, feel free to contact EXAIR or any Application Engineer.

Cody Biehle
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

## Sound Power Level and Sound Pressure

Energy…all day (and night) long, we humans are surrounded by – and bombarded by – all kinds of energy. Sometimes, the effects are pleasant; even beneficial: the warmth of the sun’s rays (solar energy) on a nice spring day is the sure-fire cure for Seasonal Affective Disorder, and is also the catalyst your body needs to produce vitamin D. Good things, both. And great reasons to get outside a little more often.

Sometimes, the effects aren’t so pleasant, and they can even be harmful. Lengthy, unprotected exposure to that same wonderful sun’s rays will give you a nasty sunburn. Which can lead to skin cancer. Not good things, either. And great reasons to regularly apply sunblock, and/or limit exposure if you can.

Sound is another constant source of energy that we’re exposed to, and one we can’t simply escape by going inside. Especially if “inside” is a factory, machine shop, or a concert arena. This brings me to the first point of today’s blog: sound power.

Strictly speaking, power is energy per unit time, and can be applied to energy generation (like how much HP an engine generates as it runs) or energy consumption (like how much HP a motor uses as it turns its shaft) For discussions of sound, though, sound power level is applied to the generation end. This is what we mean when we talk about how much sound is made by a punch press, a machine tool, or a rock band’s sound system.

Sound pressure, in contrast, is a measure of the sound power’s intensity at the target’s (e.g., your ear’s) distance from the source. The farther away you get from the sound’s generation, the lower the sound pressure will be. But the sound power didn’t change.

Just like the power made by an engine and used by a motor are both defined in the same units – usually horsepower or watts – sound power level (e.g. generation) and sound pressure (e.g. “use” by your ears) use the same unit of measure: the decibel.  The big difference, though, is that while power levels of machinery in motion are linear in scale, sound power level and pressure scales are logarithmic.  And that’s where the math can get kind of challenging.  But if you’re up for it, let’s look at how you calculate sound power level:

Where:

Wis reference power (in Watts,) normally considered to be 10-12 W, which is the lowest sound perceptible to the human ear under ideal conditions, and

W is the published sound power of the device (in Watts.)

That’s going to give you the sound power level, in decibels, being generated by the sound source.  To calculate the sound pressure level:

Where:

Lis the sound power level…see above, and

A is the surface area at a given distance.  If the sound is emitted equally in all directions, we can use the formula for hemispheric area, 2πrwhere r=distance from source to calculate the area.

These formulas ignore any effects from the acoustic qualities of the space in which the sound is occurring.  Many factors will affect this, such as how much sound energy the walls and ceiling will absorb or reflect.  This is determined by the material(s) of construction, the height of the ceiling, etc.

These formulas may help you get a “big picture” idea of the sound levels you might expect in applications where the input data is available.  Aside from that, they certainly put into perspective the importance of hearing protection when an analysis reveals higher levels.  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.