Wave Energy, Power, and Intensity
Wave intensity is time-averaged power per area normal to propagation; for a linear harmonic wave in a fixed medium it is proportional to amplitude squared, and a lossless spherical wave has intensity proportional to 1/r squared.
Why this shows up in the exam
Loudness and detector-intensity ratios · Amplitude scaling with distance · Energy transport by string or sound waves
Learn the idea
Wave energy flow grows with amplitude squared and spreads according to geometry. A larger oscillation carries disproportionately more energy; a spherical source shares fixed power over ever larger spheres, while an ideal plane wave does not geometrically spread.
🧠 Memory hook: Double amplitude means four times intensity, not twice.
Get this one clearly and it pays off every single time it shows up in the paper. 🎯
Formulas & facts to keep ready
- I = P_avg/A — definition of intensity
- I proportional to A² omega² — harmonic-wave scaling in one fixed medium
- I_spherical = P/(4pi r²) — geometric spreading from an isotropic point source
How to approach it
- 1Identify whether waves are coherent
- 2Use amplitude or area scaling as appropriate
- 3Check power conservation over the wavefront
Common slip-ups that cost marks
- •Adding intensities for coherent waves before considering phase
- •Using inverse distance instead of inverse-square intensity
- •Confusing particle energy with transported power
🌟 That's the whole idea — you've got this. Try the practice set below; every question you attempt makes it stick a little harder.
Original chapter practice
Original questions for this chapter, not past-paper questions or an exact mapping to this individual concept.
A mass of 1 kg is attached to a spring of force constant 100 N/m. Find the angular frequency of small oscillations.
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