PHY055 · Waves & Acoustics · Classes 11–12 + College
Sound intensity
Objective: To study how sound intensity falls with distance from a source (the inverse-square law).
🧰 Apparatus
- Loudspeaker with a signal generator
- Sound level meter (or phone app)
- Measuring tape
- Open space or large hall
📐 Formulas and SI units
I = P / (4π r²) (W/m²)
L = 10 log₁₀(I / I₀) dB, I₀ = 10⁻¹² W/m²
💡 Theory
A small source spreads its power over a growing sphere of area 4πr², so the intensity I = P/(4πr²) falls as 1/r²: twice as far gives a quarter of the intensity. Loudness is measured in decibels, L = 10 log₁₀(I/10⁻¹² W/m²); a quarter of the intensity is 6 dB quieter.
🪜 Procedure
- Play a steady tone at fixed volume.
- Measure the sound level 1 m from the speaker.
- Repeat at 2, 4 and 8 m along a straight line.
- Convert dB to intensity and plot I against 1/r².
- Check the drop of about 6 dB per doubling of distance.
📋 Observations Simulated values
✅ Result and conclusion
A 10 W source gives 0.199 W/m² (113 dB) at 2 m; at 4 m it is a quarter of this (107 dB).
🔬 In a real lab
Echoes from walls and the floor add to the sound indoors, so the drop is slower than 1/r² unless measured outdoors.
⚠️ Safety
Keep levels below 85 dB for long exposure; never put ears close to a loud speaker.
❓ Quick check
1. Tripling the distance makes I…
2. Unit of intensity?
3. Doubling the distance lowers the level by about…
🏋️ Practice
EasyP = 4π W, r = 1 m. I?
Answer: 1 W/m²
MediumSame source at 2 m?
Answer: 0.25 W/m²
ChallengeI = 10⁻⁶ W/m². Level?
Answer: 60 dB