The Spread of Acoustic Energy
Sound Intensity ($I$) is defined as the acoustic power ($P$) carried by sound waves per unit area in a direction perpendicular to that area. It is measured in Watts per square meter ($\text{W/m}^2$).
Imagine a speaker floating in the middle of an empty room. As it emits sound, the acoustic energy spreads outward in all directions, forming an expanding sphere. Because the surface area of a sphere grows with the square of its radius ($A = 4\pi r^2$), the sound intensity drops off rapidly as you move away.
The Inverse Square Law
Sound intensity follows the Inverse Square Law. If you double your distance from the speaker, the sound intensity doesn't just cut in half—it drops to one-quarter of its original strength. If you move three times further away, it drops to one-ninth.
The Formula
Example Calculation
A loud speaker outputs $50 , \text{Watts}$ of acoustic power. You are standing $10 , \text{meters}$ away.
- Calculate Area of the Sphere: $4 \times \pi \times 10^2 = 4 \times 3.1415 \times 100 \approx 1256.6 , \text{m}^2$.
- Divide Power by Area: $50 / 1256.6 \approx 0.0398 , \text{W/m}^2$.
The sound intensity at your position is approximately $39.8 , \text{mW/m}^2$.