Waves & Sound
Decibel scale at the ear
A louder source raises the decibel level at a fixed distance.
Decibel scale at the ear — interactive Waves & Sound simulation. A louder source raises the decibel level at a fixed distance. Free browser-based virtual physics lab with live SI measurements and a guided tutorial.
Decibel scale
The decibel scale compresses a huge range of intensities into manageable numbers using a logarithm.
Sound level β = 10 log₁₀(I/I₀) dB. A 10 dB increase means ten times the intensity. Louder sources raise β at a fixed distance.
- β = 10 log₁₀(I/I₀)
- Δβ = 10 log₁₀(I₂/I₁)
Investigation brief
Plan the question before you open the lab
The brief mirrors the prerendered page: driving question, competing predictions, variable roles, governing laws, setup, analysis and extension prompts remain visible and in this order.
Driving question
Sound intensities that humans can hear span a factor of a trillion, from a whisper to a jet engine. Why do we measure loudness in decibels instead of directly in W/m²?
Predictions to weigh
- Decibels use a logarithmic scale, so equal dB steps correspond to equal multiplicative jumps in intensity.
- Decibels are just a linearly rescaled version of W/m² for convenience.
- Decibels measure something physically different from intensity.
Variable roles
What you set:
- Distance r (m)
What you measure:
- Intensity I (µW/m²)
- Sound level β (dB)
How the investigation runs
- Open the sound-decibel preset and press Reset. The source radiates 0.12 W in all directions.
- Enable the intensity and sound-level readouts at the observer.
- Set the observer's distance from the source for each trial and record the intensity and sound level.
Governing equation
Sound Level in Decibels — L = 10·log₁₀(I/I₀)
The decibel scale compresses intensity's huge dynamic range using a base-10 logarithm relative to the quietest audible intensity I₀ = 10⁻¹² W/m², so each +10 dB represents a ×10 jump in actual intensity.
What the printable worksheet asks students to work out
- For one trial, compute I = P/(4πr²) using P = 0.12 W (report in µW/m², 1 µW/m² = 10⁻⁶ W/m²), then β = 10·log₁₀(I/I₀) with reference intensity I₀ = 10⁻¹² W/m². Compare both to the table.
- Even though your closest and farthest trials differ in intensity by a factor of 16, the sound-level column changes by only about 12 dB between them. Explain why, using the logarithm in the formula.
Where this shows up beyond the lab
- The reference intensity I₀ = 10⁻¹² W/m² is defined as roughly the quietest sound a human can hear (0 dB). Using the formula, what sound level would a listener measure exactly at the threshold intensity?
- Every +10 dB corresponds to a ×10 increase in intensity, not a doubling. Using the formula, roughly how many dB does an intensity that doubles (×2) actually add?
- AP Physics 2 — Unit 14: Waves, Sound, and Physical Optics
- IB Physics — C.2 Wave model
- General High School Physics — Waves & sound
- NGSS High School Physics — Wave properties
- Welcome to Sound Decibel
- Select the observer
- Press Play
- Logarithmic loudness
- Open the Properties panel
- You did it!
Open the interactive simulation to build the scene, press Play, and explore with live measurements and a guided tutorial.