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What is sound? Sound is the brain’s way of registering extremely small variations in pressure as measured by the ear. The ear is capable of detecting pressure changes that occur roughly in the range of 20 times per second all the way up to about 20,000 times per second. Most often, the ear monitors air pressure although it’s possible that water may come in direct contact with the eardrum, too.

How sensitive is the human ear? The human ear can detect pressure changes as low as 0.0000001 inches of water pressure. This is equal to 0.00000000361 pounds per square inch or 0.0000249 Pascal. In other terms, this is about 0.0000000246% normal atmospheric pressure. Suffice it to say the ear is extremely sensitive.

Fortunately for us, the ear is not a linear device. If ears were linear, we would only be able to tolerate a very small range of sound. Instead, the ear works as a logarithmic device. This means when faced with ten times the sound pressure, our ear perceives a sound only twice as loud. The ear is also not linear with respect to frequency. The ear’s peak sensitivity occurs in the range of 1000 to 6000 cycles per second. Coincidence or not, this also matches the typical frequency of human speech. At frequencies lower than 1000 Hz and higher than 6000 Hz, the ear’s sensitivity decreases substantially.

How do fans generate noise? There are many components to a fan’s noise, but two are truly important. The first is the motion of the fan blades. The second is “white noise” associated with random airflow. Say you’ve got a 7000 rpm fan using seven blades. You may also have a fan guard with four radial wires and some circumferential wires. If you had a means to count the number of blades that pass a given point in one second, you’d get 7000 * 7 / 60 = 817 blades per second. I’m no music major, but if memory serves this is somewhere above a middle-“C”. If you take 817 blades per second time four wires on the fan guard, you get 3268 cycles per second. This is near the peak sensitivity range of the human ear. No wonder some high-speed fans sound so annoying. The same number of blades on a 3800 rpm fan yields 443 blades per second and 1772 cycles per second. This “pitch” from the “blades per second” is the main noise you hear from a fan.

You will also hear multi-frequency “noise” from random airflow. This is the dull “whoosh” sound associated with fans. This white noise gets worse with higher airflow and when stationary items are mounted close to the fan. Finally, you’ll hear other specific frequencies depending on the fan’s surroundings, like the fan guard and heat sink. The severity of these miscellaneous sounds depends on many factors including the relative location of the fan to its surroundings and the acoustic properties of the case.

How is (fan) sound measured? This is where things begin to break down. There is actually a code (ACMA 300) for testing fans, but even this is subject to error. The goal of testing is to establish an objective measure of a fan’s sound output. Some variation still occurs, however, such that decibel readings should not be taken as an absolute. This problem is compounded when the fan is placed in a computer as many other factors come into play. The fan surroundings, mounting, and distance from the observer all affect the final perceived sound.

By now you’re probably wondering if the sound ratings of fans have any true meaning at all. The answer is a definite yes, but it’s not enough to compare dBA to dBA. One needs to consider the primary pitch of a fan’s noise, too. As a general rule, multiply the RPM by the number of fan blades. The lower this number, the lower the primary pitch and the less annoying the sound will be for a given dBA.

How about combining fans? There is no way to analytically determine the sound output from a specific location even for a single fan let alone multiple fans. There is, however, a rule-of-thumb for adding sound. With fans of equal specification, adding an extra fan will increase perceived noise by 3 dBA.

When one fan is significantly louder than the other or the pitches are different, it is not as easy to add decibels. Again, as a general rule when one fan is 4 dBA louder than the other fan, the quieter fan will add about 1.5 dBA to the total. When one fan is 10 dBA louder than the other fan, the quieter fan will add less than 0.5 dBA to the total.

How about quieting fans? We know how dropping a fan’s voltage affects its speed and flow rate, but what does it do to a fan’s noise production?

Qualitatively speaking, it does two things. First, it lowers the overall noise energy of the fan. Second, it drops the primary pitch frequency. Dropping the primary pitch frequency makes the noise seem less annoying and also decreases the dBA. This is because the human ear is most loses sensitivity as frequency decreases.

Quantitatively, the question is more difficult. As a guess, we could assume that noise energy is proportional to drive power. This means that the noise energy of a fan would trend to the cube of its rpm. If we drop a fan from 12 volts to 7, the rpm drops by 42%. The fan power drops by 80% (1 – (7/12)^3). Now we need to turn to the equation relating sound energy to decibels.

General Fan Performance Guide - Cases and Cooling 7

Here our ratio of powers equals 0.2 (20% of the original power). The dB resulting from this calculation is about –14 dB. This represents an approximate decrease in sound power level due to the fan voltage change. Depending on the fan rpms involved, you will see an additional perceived drop due to the ear’s sensitivity versus frequency. The resulting dBA decrease will be as much as 3 decibels more than indicated by the equation above.

The other guess would be that sound power is proportional to fan rpm. In this case, our sound power would drop linearly with fan voltage. Using the above example of 7 volts, our sound power would drop by 42%. The dB resulting from the equation is a drop of about 5 dB. Again, you drop an additional 3 decibels due to the frequency change. The total drop would be around 8 dBA.

I’m out on a limb here and will re-emphasize that I am making the assumption that sound power is proportional to fan power or fan rpm. The right answer probably lies somewhere between these two estimates. If someone is willing to do a little testing in this department, I’d be curious to “hear” your results.

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