Wave Property Relationships

Steps:

• Recall wave speed formula: v = f λ, where v is constant for sound in air.
• Use v = f λ to derive f ∝ 1/λ, confirming inverse proportionality.
• Intensity I ∝ (amplitude A)² from energy considerations.
• Period T = 1/f by definition.

Why A is correct:

• Amplitude determines wave energy and loudness, but is independent of wavelength, which depends on frequency for fixed speed (v = f λ).

Why the others are wrong:

• B is correct: f ∝ 1/λ from v = f λ.
• C is correct: I ∝ A² as intensity scales with energy, proportional to amplitude squared.
• D is correct: T = 1/f defines period as inverse of frequency.

Final answer: A