# Jet Engines and Decibels

I’m taking a class on drawing and one student drew two men talking behind two jet engines.

Elizabeth commented, “on a practical note, how’s he going to hear the fellow behind him? Protective ear gear, not looking at each other, an approximate 130db noise level from the engine…”

Tim replied, “They have wireless y’know. And anyway there’s two engines so that’d be 260dB!”

My response:

Cool drawings, might have to correct your acoustics statement though.

Two engines at 130 dB does not equal 260 dB. If we assume that each engine generates 130 dB, it would be more like 133 dB for two engines.

Decibels are not a linear system. It’s more like the Richter scale for earthquakes. That allows our ears to hear a greater range of intensity.

Let’s say we have one saxophone playing something compared to 10 saxophones playing that same thing in unison.

Then 10 saxophones in unison would sound twice as loud as the one saxophone.

dB level = 10 log(I/I0)

Where I0 is generally the threshold of hearing for humans.

Using a property of logs (a is the base, ten in this case)

loga (xy) = loga x + loga y

If you double the intensity, then you add 10log(2) to the original dB level. That means adding about 3 dB to the original 130 dB to get 133 dB. (That’s if the two engines are in unison)

Elizabeth saying approximately 130 dB is actually fairly accurate.