Intensity: the Energy and Power Carried by a Wave
A wave carries power proportional to the square of its amplitude, and intensity is that power spread over area. Spreading in three dimensions is why intensity falls with the square of the distance.
What a learner can do afterwards
- Relates the power carried by a wave to its amplitude and frequency
- Applies the inverse square law to a source radiating into space
- Converts between intensity and the decibel scale for sound
1 · Read
For a string or sound wave, power grows as the square of amplitude times the square of frequency. Double the amplitude and power quadruples. Intensity is that power spread over area, measured in watts per square metre.
A siren pours out fixed power that spreads over an ever growing sphere. Intensity therefore falls as one over distance squared. Double the distance and the intensity drops to a quarter.
Stand twice as far from a siren and each patch of air gets one quarter of the power, with no absorption needed. The sound fades because the same power spreads thin.
Sound loudness uses decibels: a rise of 10 dB means ten times the intensity. Two such rises in a row mean one hundred times.
Power follows amplitude squared times frequency squared, and distance spreads it over one over r squared.
2 · Watch
Take it off screen
Where it sits
Where this leads
Jobs that lean on this skill. Follow one to see everything it is built on.
8 questions wait behind this lesson, each with its answer explained. Every answer feeds the sky: stars light as they are learned, and dim when it is time to come back.