Proportionality → ratio, always
● VERBATIM — examined word-for-wordI ∝ y₀² is not an equation — solve by ratio: I₂/I₁ = (y₀₂/y₀₁)². If P and A are both unknown, I = P/A is unusable; ratios still work. Amplitude ratio = √(intensity ratio) — square/root in the right direction.
What this actually means
A proportionality has no equals sign, so numbers cannot be plugged in directly. Divide two instances instead: I₂/I₁ = (y₀₂/y₀₁)², and every unknown constant cancels.
Going the other way, the amplitude ratio is the square ROOT of the intensity ratio. Halve the amplitude, quarter the intensity; four times the intensity means the amplitude doubled.
When P and A are both unknown, I = P/A is a dead end, but ratios still close the question. That is the whole method.
Squaring or rooting in the wrong direction — amplitude ratio is the square root of the intensity ratio.
Prove it — watch it be true
- Note the intensity meter, then press A ×2
- The meter shows ×4: the ratio (2)² in action
- Reverse it: to halve intensity you need A divided by √2, not by 2