Wave intensity scales with amplitude squared and power with area

Steps:

• Original intensity I ∝ A²; power E = I × S.
• New amplitude 2A gives new intensity I' = (2A)² / A² × I = 4I.
• New area S/2 reduces the area factor by half.
• New power = 4I × (S/2) = 2(I × S) = 2E.

Why B is correct:

• Wave power equals intensity times area; intensity ∝ amplitude², so doubling amplitude quadruples intensity, but halving area halves the power, netting 2E.

Why the others are wrong:

• A: Quadruples intensity but ignores area halving.
• C: Assumes no net change, ignoring both amplitude increase and area reduction.
• D: Considers only area halving, ignoring amplitude effect.

Final answer: B