Waves & Sound
Sound intensity vs distance
Intensity falls as 1/r² — move the observer and watch I and L change.
Sound intensity vs distance — interactive Waves & Sound simulation. Intensity falls as 1/r² — move the observer and watch I and L change. Free browser-based virtual physics lab with live SI measurements and a guided tutorial.
Inverse-square intensity
Sound intensity falls off as 1/r² from a point source in three dimensions.
Power spreads over a spherical surface area 4πr², so intensity I = P/(4πr²). Doubling distance quarters the intensity.
- I = P/(4πr²)
- I ∝ 1/r²
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
A speaker radiates sound equally in all directions. If a listener moves twice as far away, how much does the sound intensity drop?
Predictions to weigh
- Intensity drops to 1/2 — it falls off linearly with distance.
- Intensity drops to 1/4 — it falls off with the square of distance.
- Intensity stays the same regardless of distance.
Variable roles
What you set:
- Distance r (m)
What you measure:
- Intensity I (µW/m²)
How the investigation runs
- Open the sound-intensity preset and press Reset. The source radiates 0.05 W in all directions (spherical spreading).
- Enable the intensity readout at the observer.
- Set the observer's distance from the source for each trial and record the intensity.
Governing equation
Inverse-Square Law for Sound Intensity — I = P/(4πr²)
Power radiated equally in all directions spreads over a sphere of area 4πr². Intensity — power per unit area — therefore falls off as 1/r² with distance from the source.
What the printable worksheet asks students to work out
- For one trial, compute I = P/(4πr²) using P = 0.05 W, expressing your answer in µW/m² (1 µW/m² = 10⁻⁶ W/m²). Compare to the table.
- Explain, using the surface area of a sphere 4πr², why sound power spreading outward makes intensity fall off as 1/r² rather than 1/r.
Where this shows up beyond the lab
- Doubling distance quarters the intensity, but loudness (in decibels) only seems to drop by a fixed amount each time distance doubles. Look at the sound-decibel experiment — what kind of function turns a ×4 intensity ratio into a fixed dB difference?
- This experiment assumes the source radiates equally in every direction. A megaphone instead focuses sound into a narrow cone. How would you expect the intensity 1/r² law to change for a focused source at the same distance?
- 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 Intensity
- Select the observer
- Press Play
- Weaker with distance
- 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.