Intensity proportional to amplitude squared

Steps:

• Intensity I of sound waves is proportional to the square of the amplitude a, so I ∝ a².
• The given formula shows I = P / (4πr²), so I ∝ 1/r².
• Substitute: a² ∝ 1/r².
• Take square root: a ∝ 1/r.

Why A is correct:

• For spherical waves, intensity decreases as 1/r² due to surface area, and since I ∝ a², amplitude a must decrease as 1/r to match.

Why the others are wrong:

• B: a ∝ 1/√r implies a² ∝ 1/r, but I ∝ 1/r², so mismatch.
• C: a ∝ r implies amplitude grows with distance, violating energy conservation.
• D: a ∝ r² implies even faster growth, impossible for spreading waves.

Final answer: A