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Physics · University

Intensity-level difference

The ratio is an intensity ratio. Pressure-amplitude ratios use 20 log₁₀ under matched impedance conditions.

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Method and conditions

The ratio is an intensity ratio. Pressure-amplitude ratios use 20 log₁₀ under matched impedance conditions.

ΔL = 10 log₁₀(I₂/I₁)

Worked examples

Two sound intensities satisfy I₂/I₁ = 117. Calculate L₂ − L₁ in decibels. Round the final result to 4 decimal places if needed. Answer in dB.

Apply 10 log₁₀(117); the reference intensity cancels in the difference.

20.6819 dB

Two sound intensities satisfy I₂/I₁ = 230. Calculate L₂ − L₁ in decibels. Round the final result to 4 decimal places if needed. Answer in dB.

Apply 10 log₁₀(230); the reference intensity cancels in the difference.

23.6173 dB

Try it

  1. Two sound intensities satisfy I₂/I₁ = 77. Calculate L₂ − L₁ in decibels. Round the final result to 4 decimal places if needed. Answer in dB.

  2. Two sound intensities satisfy I₂/I₁ = 243. Calculate L₂ − L₁ in decibels. Round the final result to 4 decimal places if needed. Answer in dB.

Check your work

Answers and marking notes
  1. 18.8649 dB

    Apply 10 log₁₀(77); the reference intensity cancels in the difference.

  2. 23.8561 dB

    Apply 10 log₁₀(243); the reference intensity cancels in the difference.

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