Sound Intensity Calculator Formula

Understand the math behind the sound intensity calculator. Each variable explained with a worked example.

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Formulas Used

Sound Intensity

intensity = power / area

Intensity Level

intensity_db = 10 * log10(power / area / 1e-12)

Variables

VariableDescriptionDefault
powerSound Power(W)0.01
areaArea(m²)12.566

How It Works

Sound Intensity

Sound intensity is the power carried by a sound wave per unit area perpendicular to the propagation direction.

Formula

I = P / A

For a point source radiating uniformly, A = 4*pi*r². The intensity level in decibels is L = 10 * log10(I / I_0) where I_0 = 10^-12 W/m² is the threshold of hearing.

Worked Example

A speaker emitting 0.01 W of sound power, measured at 1 m (sphere area = 4*pi*1² = 12.566 m²).

power = 0.01area = 12.566
  1. 01I = P / A
  2. 02I = 0.01 / 12.566
  3. 03I = 7.958 x 10^-4 W/m²
  4. 04L = 10 * log10(7.958e-4 / 1e-12)
  5. 05L = 10 * log10(7.958e8)
  6. 06L = 89.0 dB

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