Intensity proportional to amplitude squared

Steps:

• Intensity I is proportional to amplitude squared: I ∝ A².
• Original wave: I = k A², where k is a constant.
• New intensity I' = I/4 = k (A')².
• Solve for A': (A')² = A² / 4, so A' = A / 2.

Why B is correct:

• Wave intensity follows I ∝ A², so reducing intensity by a factor of 4 requires halving the amplitude.

Why the others are wrong:

• A: Doubling amplitude increases intensity by 4 times, not decreases it.
• C: Halving amplitude twice (to A/4) reduces intensity to I/16.
• D: Reducing amplitude to A/16 reduces intensity to I/256.

Final answer: B