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The Acoustic Equation

When it's safe to visit large indoor spaces again, we encourage you to pay attention to the acoustics. Like us, you probably take it for granted. But, the truth is, it's a miracle that lecturers can be heard from the back of an auditorium, or the words of your favorite song leave a singer’s lips and reach your ears in one piece. This is because sound acts completely differently from one room to the next. And up until the 1900s we had no idea how a building’s architecture influenced its acoustics. This means that for centuries people built lecture halls with their fingers crossed, hoping the speaker’s voice wouldn’t be swallowed up by the roof or splattered across the room in a thousand annoying echoes.

As you can imagine, this gamble was an expensive one. So, when Harvard University built its Fogg Art Museum in 1895 and discovered the lecture hall was just one big reverb machine, they enlisted the help of Wallace Sabine - a physics lecturer - to find a solution. He meticulously tested the reverb in countless rooms on campus and recorded the effects that various materials had on the acoustics. He was so meticulous that he reportedly scrapped a swathe of recordings after realizing his clothes were screwing up the measurements. No, he didn’t continue the experiments naked, he just wore the same outfit every time he took measurements. 

Sabine conducted these experiments for years until he finally produced the aptly named, Sabine Equation. His equation allowed architects to predict a room’s reverb based on the surface area of the structure and the materials used. For example, the architects of St. Thomas Church in Manhattan wanted the building to have a gothic aesthetic but without the reverb. So, they asked Sabine to use his equation and help design the room with those acoustics in mind. He plugged in the numbers, and carefully positioned absorbent ceramic tiles throughout the building. No surprise, it was a success! #mathworks

However, a room's acoustics is not immure to the fickle world of fashion. In the 70s, people wanted a bit more reverb in their buildings, so the church’s tiles were painted to reduce their absorbent quality.

Today, we can use fancy technology to manipulate a room's reverb, but at the core of all acoustic design sits Sabine’s equation. Happy listening.

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Image by Wokandapix


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