← all cardsTopic 11 · Wave Motion · Energy & intensity
The intensity chain from SHM
● VERBATIM — examined word-for-wordEach particle is an SHM oscillator: E = ½mω²y₀² → energy ∝ f²y₀² → wave = sum of oscillating particles → I ∝ y₀² at constant f, I ∝ f²y₀² in general. Doubling frequency at fixed amplitude ALSO quadruples intensity. Quote the SHM chain when asked to justify.
I ∝ f²y₀² · I₂/I₁ = (y₀₂/y₀₁)²(f₂/f₁)²What this actually means
Each particle stores E = ½mω²y₀² as an SHM oscillator, and a wave is a train of such oscillators. Since ω = 2πf, that energy scales with f²y₀², and so does the intensity.
At fixed frequency this collapses to the familiar I ∝ y₀². But doubling frequency at fixed amplitude also quadruples intensity, a fact most students have never confronted.
When the question says 'explain', quote the chain: SHM energy formula, so E ∝ f²y₀², so I ∝ f²y₀².
Prove it — watch it be true
- Press the A ×2 button: the I ∝ f²A² meter jumps by 4
- Press the f ×2 button: it jumps by 4 again
- Both squares are real — amplitude is not the only lever