An angular frequency wave ω0 has an average power P0. If your angular frequency increases by 20%, find the percentage by which its power increases.

44%

Explanation:

The average power of a wave is directly proportional to the square of the frequency.

P ∝ ω²

Writing a proportion:

P₁ / P₀ = ω₁² / ω₀²

P₁ / P₀ = (1.2 ω₀)² / ω₀²

P₁ / P₀ = 1.44

P₁ = 1.44 P₀

The power increases by 44%.

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