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The Decibel (dB) Scale: A Logarithmic Scale for Sound
See how the decibel scale compresses huge intensity ratios into small, manageable numbers using logarithms, with the formula and worked examples.
What You'll Learn
The decibel (dB) scale is a logarithmic scale used to compare sound intensities that can span trillions to one.
The core formula is L equals 10 times the log base 10 of the intensity ratio, written as L = 10 log10(I / I0).
Every increase of 10 dB means the sound intensity is 10 times greater, not just 10 units louder.
Converting between dB and intensity ratio uses the same log-to-exponential-form skills seen elsewhere in logarithms.
Worked examples show both directions: finding dB from an intensity ratio, and finding the ratio from a dB value.
What You'll Practice
1
Using the formula to find intensity ratios from given decibel measurements
2
Comparing sounds with different decibel levels (whispers, piano, etc.)
3
Calculating ratios that result in large and small decimal values
Why This Matters
The dB scale is used everywhere from audio engineering to environmental noise regulations. Understanding logarithmic scales helps you grasp why a small decibel increase means a huge jump in actual loudness, a concept that appears in many scientific fields and real-world applications.
Before You Start — Make Sure You Can:
This Unit Includes
2 Video lessons
Practice exercises
Learning resources
Skills
Logarithmic Scale
Decibels
Exponential Functions
Ratios
Sound Intensity
Applied Mathematics
OH Curriculum Aligned