# Acoustic calculation

Hi all,
In the PPD practice exam 1 there is a acoustic question that I can’t figure out how to solve it. In a nutshell “There are two identical fans that together produces 60 dB of sound. If one of the fans is removed, then the new dB level will be 57dB”.
Here is the question explanation “Reducing sound intensity by half reduces it by 3 dB. 60-3=57” but it still doesn’t make sense to me.
Can anyone explain to me how this works? Is there a formula?

Thank you!

Nathalia

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Hi @nathaliavs and welcome to the ARE Community!

Let’s get one of our expert architects to better explain how it works! @coachbryanhadley do you mind jumping in?

Hi @nathaliavs,

This question is asking you to recall the 3 db rule of sound intensity, which is this: If you increase the intensity of a sound by 3db it will double the audible noise, and if you reduce it by 3db it will halve the amount of audible noise.

Recall from your environmental controls classes that sound intensity is not linear; it is logarithmic. The formula to calculate a difference in two sound intensities is this: 10 Log 10 (S1 / S2), where S1 and S2 are the intensities of your two sounds.

I found a nice, fairly simple explanation for you on Encyclopedia Brittanica: https://www.britannica.com/science/decibel

More generally I would look at the NCARB ARE 5.0 Handbook for any formulas that you will be expected to know. This particular formula is not listed by NCARB but this 3db rule is an important principle to be familiar with.

Hope it helps,

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I actually have a question about this question, as well. According to MEEB (Chapter 17, Table 17.3), if you increase a sound by 10 dB it doubles the subjective loudness, and if you decrease by 10dB it halves the loudness. It says that 3db doubles signal intensity. Can you clarify how these different measurements are different and when they would be used?

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Hi @charlotte.m.mckernan & welcome to the ARE Community!

@coachglennparks do you mind providing clarification for Charlotte?

Hi Charlotte,
Consider your ears’ sensitivity to sound in the short term and long term. Something abruptly louder for a short amount of time allows you time to recover to the norm. Something increasingly louder over a period of time may require a little while for you to notice that your ear has been exposed to louder and louder noise, but depending on how much louder will require a logarithmic scale than a linear scale to be useful. As a wave metaphor, consider seismic wave measurements that are logarithmic rather than linear, like the Richter scale. Why are these waves measured logarithmically rather than linearly? Is frequency and intensity of occurrence important for designing structures in high seismic zones?

A decibel is literally 1/10th of a bel, which is a relative unit used to express the ratio of one value of a power or root-power quantity to another, on a logarithmic scale. So, these are used to quantify the range of sounds that impact human hearing. Like earthquake measures on a Richter scale describe potential impacts to buildings, decibels measure impacts to our ears on a standard scale.

An increase of 3dB doubles the sound intensity but a 10dB increase is required before a sound is perceived to be twice as loud. Therefore a small increase in decibels represents a large increase in intensity. The so-called, “3db rule” addresses the human perception and impact of sound (or noise, which is any unwanted sound) on the ear’s “structure.”

Architectural design presumes, typically, to provide a healthful environment. When data provided in terms of exposure are presented in decibels, we can select materials with various sound absorbing qualities and arrange them in deflective geometries to mitigate unhealthful noise.
-Coachglenn