A wave on a uniform string has amplitude A₀, angular frequency ω₀ and average power P₀ at x = 0. At x = ℓ the average power has fallen to P₀/2. Find the angular frequency and amplitude at x = ℓ.
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Question

A wave on a uniform string has amplitude A₀, angular frequency ω₀ and average power P₀ at x = 0. At x = ℓ the average power has fallen to P₀/2. Find the angular frequency and amplitude at x = ℓ.

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G1 Physics · Accepted Answer

Step 1: The source frequency does not change during propagation, so ω = ω₀. Step 2: For the same string P̄ ∝ ω²A². With P̄ reduced from P₀ to P₀/2 at unchanged ω, A² = A₀²/2. Hence A = A₀/√2. Final: A.