The Basics of Fan Sound (FA/121-03)

October 1st, 2003

Fan sound is a very important consideration in the selection and application of fans. In spite of this, fan sound continues to be one of the most misunderstood topics in the air handling industry.

In an effort to provide a better understanding and point of reference on how fan sound is developed, rated, applied and controlled; this is the second article in a series of four articles covering this topic.

Part 1   Understanding the Development of Fan Sound Data and the Product Line Rating Process (FA/120-02)

Part 2   The Basics of Sound (FA/121-03)

Part 3   Radiated Sound (FA/122-03)

Part 4   Sound Criteria, Attenuation Techniques and Preventive Measures to Limit Sound Problems (FA/123-03)

This article discusses the nature of sound, sound terminology, different methods of rating fans for sound and typical calculations that most people take for granted due to computerization.

What is sound?

We are all aware that energy comes in many different forms; light, heat, electrical, nuclear, sound etc. However, unlike the others, sound is characterized as a form of energy resulting from vibrating matter. As the matter vibrates, it creates waves in the surrounding medium (air, water, metal etc.) that have alternating compressions and rarefactions. In air, this represents a very small change in the barometric pressure to which our ear drums react. Our ears distinguish one sound from another by its loudness and pitch. Loudness is the amplitude or amount of sound energy reaching our ears. Pitch is the relative quality of the frequency content made up of pure tones as well as broadband sounds. We typically use the pitch to identify the source of a sound. However, both the loudness and pitch may vary depending upon where we are located relative to the sound and the surrounding environment.

What is fan sound?

Fan sound represents a characteristic combination of frequencies made up of many different individual components. It is a by-product of many different aerodynamic mechanisms going on inside the fan. Some of these include vortex shedding, eddy formations, turbulence and discrete tones such as the blade frequency. There are also various combinations of mechanical sound coming from drives, motors, bearings etc. All of these logarithmically combine to form a sound spectrum recognizable to the ear as being a fan.

This concept is illustrated in Figure #1. The lower sound spectrum is one-third octave band sound level data from a twenty-four inch airfoil fan. Note that there are individual peaks that are prevalent at various frequencies. These peaks correspond to the sound contribution of individual components such as the blade frequency, motor, drives or even a panel resonance from the scroll. It is these tones that our ears characterize as fan sound. Please remember, fan sound comes from a number of sources, aerodynamic as well as mechanical.

Figure 1

Fan Sound Power Levels (dB)
Installation Type B, Free Inlet, Ducted Outlet
24 Airfoil Single Width
4100 CFM, 1.4 SP, 870 RPM, 60% WOV

By convention, fan sound is presented on an octave band basis in accordance with ANSI standards. This makes dealing with sound less burdensome by using eight numbers versus twenty-four to define the frequency spectrum. However, when one-third octave band sound values are logarithmically added together into octave bands, the resulting sound level is higher but the individual peaks are not graphically identifiable in the new spectrum. This does not mean that they are no longer there. Your ear will still hear the tones, but the method of presentation smooths over the appearance of individual component contribution in the data. The octave band data can be further simplified to a one number system such as LwA or dBA, sones etc. However, with each simplification in the method of presentation, the identification of specific components is further reduced.

Defining fan sound

It is easier to understand fan sound using the graphical format illustrated in Figure #1. Using this figure as a reference, each of the rating parameters will be discussed. It is important to understand the concepts presented since they apply equally well for all fan sound data, not just for this specific example.

Sound power versus sound pressure

The difference between sound power and sound pressure is critical to the understanding of this subject. Most industrial and commercial ducted fan catalog data is presented in sound power levels in each of eight octave bands. However, some commercial and residential non-ducted catalog sound data is presented on a sound pressure basis using a single number rating system such as dBA or sones.

Energy for light, heat, electrical and most fan sound is provided referenced to the watt. The power produced by a light bulb, a heater or a fan are an indicator of the power produced by the source independent of the distance from the source or the environment in which it is located. As an example, a sixty watt light bulb consumes sixty watts no matter where it is screwed in. Fan sound power is the same.

Fan sound power is determined through tests conducted in accordance with AMCA Standard 300, "Reverberant Room Method for Sound Testing of Fans". Test results are provided in sound power levels in dB referenced to ten to the minus twelve watts in each of eight octave bands. This is the sound produced by the fan at its source and is independent of the fans environment.

Sound pressure levels represent the energy a microphone or our ears would receive and depends upon the distance from the source as well as the acoustical environment of the listener (room size, construction materials, reflecting surfaces, etc.). Sound pressure levels are provided in dB referenced to the microbar (.0002) or twenty micropascals.

Installation type

Published sound ratings are presented at the fan inlet, fan outlet or total sound power for the following installation types. It is important to know the installation type that best matches the actual application because sound levels are not the same for each installation.

Installation Type Configuration
A Free Inlet, Free Outlet
B Free Inlet, Ducted Outlet
C Ducted Inlet, Free Outlet
D Ducted Inlet, Ducted Outlet

Fan designation

The size and design of the fan must be identified.

Fan rating

The  AMCA Certified Ratings Program has a seal for ĝair" and a seal for ĝair and sound". A sound rating cannot exist by itself. It must have a corresponding aerodynamic rating because sound is a function of the fan rating point.

Loudness/ amplitude

Because sound loudness is referenced to very small numbers and there also is a very wide range, it is much more convenient to use the decibel. The decibel is a dimensionless number expressing in logarithmic terms the ratio of a quantity to a reference quantity. As an example, one dB represents the threshold of hearing.

Sound Power (dB) =

            10 log (sound power [watts]/10-12)

Sound Pressure (dB) =

             20 log (sound pressure [microbars]/.0002)

Sones

An alternative loudness descriptiont is sones. Sones follow a linear scale, that is, 10 sones are twice as loud as 5 sones. Use the following formula to convert sones to decibels.

dBA = 33.2 Log10 (sones) + 28, Accuracy +/- 2dBA

LwA and dBA respectively are sound power and sound pressure rating systems for most industrial and commercial fan equipment. A third single number system is used for non-ducted propeller fans and power roof ventilators called the sone. A sone is a term of loudness perceived by the ear related to a frequency of 1,000 Hz. The sone is a sound pressure term at a distance of five feet from the fan and is linear to the human ear.

Calculating sones from sound pressure level is outlined in ANSI Standard 3.4. A loudness index is obtained from a graph or calculated using a formula in the standard. The total loudness is calculated from another formula. (See example 1.) The application of sones is outlined in AMCA Publication 302.

Example 1

               
Calculation of sones
AMCA octave band no. 1 2 3 4 5 6 7 8
Sound pressure level 64 67 63 62.5 58.5 53.5 50 45.5
Loudness index 2.11 4.00 4.10 4.75 4.45 3.95 3.80 3.50
Sones = .3 (2.11+4.00+4.10+4.75+4.45+3.95+3.80+3.50) + .7 (4.75) = 12.5

 

Frequency

Frequency is the number of pressure variations per second expressed in Hertz.  One cycle per second equals one Hertz. The human ear can perceive sound between 20 Hz. and 20,000 Hz. However, fan sound is dominant between 50 Hz. and 10,000 Hz. Therefore, there is no reason to deal with frequencies outside of this range.

This frequency range for test purposes has been divided into twenty-four individual bands called one-third octave bands. Three one-third octave bands when logarithmically combined together form an octave band. An octave band is the interval between any two frequencies having a 2:1 ratio. As an example, the center frequency for the first octave band is 63 Hz. The center frequency for the second octave band is 125 Hz, third is 250 Hz. and so on up to the eighth octave band with a center frequency of 8000 Hz. The abscissa of Figure #1 illustrates the relationship between band numbers and frequency for both one-third and full octave bands.

Perceiving fan sound levels

It is important to maintain a common sense approach to looking at fan sound. Many people look at sound levels in too strict a manner without maintaining an overall perspective of their significance. From an accuracy standpoint, fan sound levels are less accurate than aerodynamic performance ratings. AMCA 300 indicates that tolerances of +/- six dB are possible in the first octave band and +/-  three dB in the remaining octave bands. When comparing sound levels a difference of three dB is barely perceptible to the human ear. A difference of five dB is enough to make a distinction as to which is louder. It takes a difference of ten dB between two sound levels to make one sound twice as loud as the other.

When looking at sound levels it is very hard to relate that sound level to a typical source; ie, something we know. Simply to provide some perspective of the loudness of some sounds, the following table contains typical sound categories and corresponding sound levels.

Sound
Category
Sound
Pressure (dB)
Threshold of Pain 140
Threshold of Discomfort 120
Conversational Speech 60
Threshold of Hearing 0

Typical sound calculations

Catalog sound power levels are provided in each of eight octave bands. Sometimes it becomes necessary to take these values and convert them to other conditions. The following sections provide guidance and examples of the most common types of calculations.

Combining sound levels

The addition of sound levels must be done on a logarithmic basis, not arithmetic. Fortunately, computers are readily available to access Greenheck's Computer Aided Selection Program (CAPS), however, this addition can be done quickly and easily by hand as well. It involves a very simple process which is performed over and over again. The chart on page 5 illustrates the amount two sound levels contribute to each other based upon the difference between them. (See examples 2 and 3.) If two sound levels are identical, the combined sound is three dB higher than either. If the difference is ten dB, the highest sound level completely dominates and there is no contribution by the lower sound level.

Sound pressure level considerations

It has been repeatedly emphasized that sound power level values are independent of the distance and acoustical environment. On the other hand, sound pressure levels are a function of the location of the source as well as the listener. To estimate sound pressure levels requires a detailed knowledge of many different parameters. Since fan manufacturers have no idea where their fans or the ultimate listener are located, they are not in a position to calculate sound pressure levels for most applications. However, over the years, in order to provide users with some idea of what sound pressure levels might be expected, a "default set of assumptions" have been made which may or may not match the actual application. This default set of assumptions have been well accepted by users to the point where many catalogs contain sound levels based upon sound pressure. The following sections outline the default assumptions and the calculation process used to obtain various catalog sound pressure levels.

Default assumptions

The following assumptions are universally used in making sound pressure level predictions.

Point source

This assumes that the listener is far enough away from the fan to consider it a point source. This is consistent with most theoretical calculations made in acoustics. The key emphasis is that the listener is not in what is called the near field.

Directivity factor

It is assumed that the fan is mounted on a floor, ceiling or wall. Therefore, it can also be assumed that there is one reflecting surface that bounces the sound waves back towards the listener. This is referred to a directivity factor of two.

Hemispherical radiation pattern

Consistent with the directivity factor, it is assumed that the sound radiates from the fan in a hemispherical radiation pattern. A spherical radiation pattern would mean that the sound radiates equally in all directions from the fan and does not have a reflecting surface.

Straight line distance

It is assumed that the sound travels in an uninterrupted straight line from the fan to the listener. In other words, the listener can look directly at the fan and see it. No ductwork is between the fan and listener. Typically a distance of five feet is selected as being reasonable.

Free field conditions

It is assumed that the sound is free to radiate outwardly in an uninterrupted manner and is not reflected from any other surface other than the floor or ceiling it is mounted upon. The sound is free to just go and go.

Constant difference between sound power and sound pressure

Based upon all of the previous assumptions, (five feet away from a point source in a hemispherical free field) it is possible to calculate the difference between sound power and sound pressure. This means that the sound pressure level is 11.5 dB lower than the sound power level regardless of octave band.

A weighting

Sound pressure levels which are heard by the human ear are based upon the "A" scale. There is a constant set of weighting factors illustrated in the following table to approximate the response of the human ear. (Refer to AMCA Publication 303-79.)

"A" weighting factors
AMCA octave band no.   1 2 3 4 5 6 7 8
"A" weighting factor  -25 -15 -8 -3 0 +1 +1 -1

It is important to realize that "A" weighting numbers are fully meaningful only when applied to sound pressure values. "A" weighting factors are sometimes applied to sound power levels which are then combined into a single number (LwA). This provides a single number for comparison between fans when sound power spectrums are provided. The LwA number cannot be verified by measurements in the field.

Typical sound level calculations

Several sound level quantities can be calculated using combinations of the previous information. These are illustrated in examples 4, 5, and 6.

Summary

Knowing values of fan sound is vitally important. They should be obtained for every fan selection and compared to available acceptance criteria up front in the design stages. This will help provide the assurance necessary for a successful application.

Example 4

Single number sound power level (LwA)
AMCA octave band no. 1 2 3 4 5 6 7 8
Sound power level 75.5 78.5 74.5 74 70 65 61.5 57
“A” weighting -25 -15 -8 -3 0 +1 +1 -1
LwA by octave band 50.5 63.5 66.5 71 70 66 62.5 56

Combining into a single number (LwA) = 75.5 dB

 

Example 5

Calculating sound pressure levels
AMCA octave band no. 1 2 3 4 5 6 7 8
Sound power level 75.5 78.5 74.5 74 70 65 61.5 57
Delta power pressure 11.5 11.5 11.5 11.5 11.5 11.5 11.5 11.5

Sound pressure level

 

64 67 63 62.5 58.5 53.5 50 45.5

Example 6

Calculating single number sound pressure level (dBA)
AMCA octave band no. 1 2 3 4 5 6 7 8
Sound power level 75.5 78.5 74.5 74 70 65 61.5 57
Delta power pressure 11.5 11.5 11.5 11.5 11.5 11.5 11.5 11.5
Sound pressure level 64 67 63 62.5 58.5 53.5 50 45.5
“A” weighting -25 -15 -8 -3 0 +1 +1 -1
“A” weighted pressure 39 52 55 59.5 58.5 54.5 51 44.5
Combining into a single number (dBA) = 64 dB
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