Sound Intensity & Decibels

Sound energy spreads out equally in every direction from its source, like ripples growing outward on a sphere. As that sphere gets bigger, the same total power is stretched over more and more area, so the intensity — power per square meter — drops off fast the farther you get, following an inverse-square pattern with distance.

I = P / (4π · r²)

I — intensity (W/m²): how much sound power passes through each square meter of area
P — power (W): the total sound energy the source emits every second
r — distance (m): how far you are from the source

A speaker emits 12.56 watts of sound power equally in all directions. Using 4π ≈ 12.56, what is the sound intensity 1 meter away?

P = 12.56 W
r = 1 m

I = P / (4π · r²)
I = 12.56 W / (12.56 · 1 m²)

I = 1 W/m²

The same 12.56-watt speaker is now measured 2 meters away instead of 1. What is the new intensity?

0.25 W/m²
0.5 W/m²
4 W/m²

A sound's intensity jumps from I₀ to 100 times I₀. How many decibels does the sound level go up?

100 dB
10 dB
20 dB