You may wonder why those of us in acoustics use decibels (dB). It’s actually much more than a calculation just used by acoustics folks: researchers in electronics and seismology fields use dB as a routine measurement, for example. Since these areas primarily focus on natural properties of matter and energy, they need the best mathematical tools for the job. If you’re interested in a much more technical understanding of how and why decibels came to be so important, I’d recommend Steve Africk’s blog post on the subject. For now, I’m going to take a step back and provide some broader context for this key measurement in acoustics.
Our ears are similar to microphones, which detect sound pressure on our eardrums. So why don’t we use the sound pressure instead? The human ear is sensitive to such a large range of sound pressures: the difference between a sound that is just perceptible to us compared to a sound that causes physical pain is about a trillion times. In the physical world, this would be similar to a range between the thickness of a single human hair to the height of the Empire State Building. That would be a whole lot of digits for us to calculate. So we first make a ratio, relating the pressure of a measured sound and dividing it by the quietest pressure that our ears can hear. Then, we take that number and use the magic of logarithms™ (not really a trademark, promise!) to squish that range down to something that’s easier for us to work with. This reduces the sound range from a trillion, down to about 100 decibels.
It’s simpler in some ways, but can add more complications when first trying to grasp this concept. Now that we have this new range, combination and comparison of decibels may seem a bit strange since you can no longer add them arithmetically (i.e. when 1 + 1 = 2 and when 100 + 100 = 200). In our world, every time the sound doubles, the increase to the sound level is 3 decibels. This means that 1 dB + 1 dB = 4 dB, and 100 dB +100 dB = 103 dB.
We further add-in the complication of how mathematical differences on paper doesn’t necessarily equate to what our ears and brains perceive as a noticeable change. While a doubling of sound pressure only produces an increase of 3 decibels on paper, it actually takes about a 10 decibel increase for normal hearing individuals (?) to perceive something as being twice as loud.
So how does this apply to the world outside of physics and hypothetical research? Let’s investigate a timely example: the Red Sox World Series Parade.
Last week, I went to the Boston Common at Tremont and Park Street and brought a sound level meter along for the ride. Throughout the parade, I measured the decibel levels of the activity around me. Here’s what I found:
So, when comparing a normal day in the commons to the parade celebration, you’re looking at an increase from about 60 to 90 decibels. Mathematically there was a thousand-fold increase in sound, but in terms of how humans perceive sound, it was 8 times as loud. Definitely a huge change either way you look at it.
With their first World Series win in half a decade, Red Sox fans certainly had a lot to celebrate last week. I can only imagine what the sound level meters would measure at a parade if they win again next year!