The Decibel

The decibel is a unit of measurement that relates the ratio of a physical value to another value and is expressed on a logarithmic scale.  The common symbol for decibel is dB.  The decibel is used as a measure for many parameters in science and engineering such as acoustics (sound), electronics (power levels) and control theory.

The decibel originates from methods used to express performance and loss in telegraph and telephone circuits.  The term ‘bel’ was coined in honor of Alexander Graham Bell, and the decibel, being 1/10th of a bel was established.

For most of us, the decibel is the familiar term relating to how loud a sound is.

With sound, the sound pressure is typically what is measured and is the local pressure deviation from the base or equilibrium atmospheric pressure, caused by a sound wave. In air, the sound pressure can be measured by a standard microphone, and is measured in pascals (Pa.)

To get to the common decibel reading we are familiar with, a little mathematics comes into play.

Capture

  • where Lp is the Sound Level in dB, prms is the measured sound pressure, and pref is the standard sound reference pressure of 20 micropascals.
  • The prms is what is measured by a microphone

Below are some representative sounds and the decibel rating – Note that sounds that are above 85 dB can cause hearing issues, and proper protection should be taken.Decibel Scale Still Photo

Some other interesting blogs about sound for you take a look at-

Measuring and Adding Sounds

Sound Power Level and Sound Pressure

Super Air Knife Math – When 72  + 72 = 75

If you would like to talk about sound or any of the EXAIR Intelligent Compressed Air® Products, feel free to contact EXAIR and myself or one of our Application Engineers can help you determine the best solution.

Brian Bergmann
Application Engineer

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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:

Sound Power Level Equation

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:

Sound Power Level to Sound Pressure Equation

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:

Working in areas that exceed these levels will require hearing protection.

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.