Amplitude variation in attenuating sound waves

Steps:

• Intensity I is proportional to amplitude squared (I ∝ A²); decreasing I means A decreases with propagation distance.
• Constant frequency f keeps wavelength λ constant, since λ = v/f and speed v is fixed in air.
• Wave spreading or absorption causes A to vary continuously along the direction of travel.
• Thus, maximum particle displacement (A) differs slightly between adjacent particles separated along the propagation path.

Why A is correct:

• Decreasing intensity requires amplitude to decrease with distance, so maximum displacement varies between particles at successive positions, per the inverse square law for spherical waves.

Why the others are wrong:

• B: Adjacent particles along propagation have a small non-zero phase difference of (2π/λ) × separation distance.
• C: Wavelength λ is the distance for a 360° phase difference; 180° corresponds to λ/2.
• D: 360° phase difference means particles are in phase, but at different distances they have different amplitudes due to attenuation.

Final answer: A