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Physics

Sound Intensity Level

Sound intensity level expresses an intensity ratio on a logarithmic scale.

β = 10 lo g_{10} (\frac{I}{I _{0}})

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Source & review

Difficulty

Intermediate

Read time

5 min

Prerequisites

Basic algebra, consistent units, and the stated model assumptions

Review statusNeeds review

Source

OpenStax, College Physics 2e, §17.3 (Paul Peter Urone and Roger Hinrichs)

OpenFormulaGraph equation reference; FormuLab adaptation details and license are provided below.

Adapted from OpenFormulaGraph, under CC BY 4.0.

FormuLab adapted wording, notation, applicability conditions and topic placement, and expanded the numerical check into a worked example.

Definition

Understanding the core concept

Sound intensity level expresses an intensity ratio on a logarithmic scale. A factor of ten in intensity corresponds to an increase of 10 dB.

Variables & Units

Understanding each component

Symbol	Meaning	Units
$β$	Sound Intensity Level	$dB$
$I$	Sound Intensity	$W/ m^{2}$
$I_{0}$	Reference Sound Intensity	$W/ m^{2}$

Real-World Applications

Where this formula is used in practice

Acoustic measurements

Express an intensity relative to a reference.

Intensity comparisons

Translate intensity ratios into level differences.

Worked Example

Step-by-step calculation with real numbers

Problem

Find the intensity level for I = 10⁻⁶ W/m² relative to I₀ = 10⁻¹² W/m².

Given

I = 0.000001 W/ m^{2}

I_{0} = 1 \times 1 0^{- 12} W/ m^{2}

Solution

β = 10 lo g_{10} (\frac{I}{I _{0}})

β = 10 \cdot lo g_{10} (\frac{( 0.000001 W/ m ^{2} )}{( 1 \times 1 0 ^{- 12} W/ m ^{2} )})

β = 60 dB

Final Answer

β = 60 dB

Formula Guide

Info

DifficultyIntermediate

Read Time5 min

PrerequisitesBasic algebra, consistent units, and the stated model assumptions

Tools

Source & review

StatusNeeds review

Last reviewedPending

Source

OpenStax, College Physics 2e, §17.3 (Paul Peter Urone and Roger Hinrichs)

OpenFormulaGraph equation reference; FormuLab adaptation details and license are provided below.

Adapted from OpenFormulaGraph, under CC BY 4.0.

FormuLab adapted wording, notation, applicability conditions and topic placement, and expanded the numerical check into a worked example.

Assumptions

• Use positive intensities with the same units and a stated reference I₀.
• The usual airborne reference is 10⁻¹² W/m²; intensity level is not automatically a frequency-weighted sound meter reading.

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Sound Intensity Level

Acoustic measurements

Intensity comparisons

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