Show that y = 3·sin(2x − 6t) satisfies the wave equation and find the wave speed. Step 1: Compute ∂²y/∂x²: ∂y/∂x = 6·cos(2x−6t); ∂²y/∂x² = −12·sin(2x−6t) = −4y. Step 2: Compute ∂²y/∂t²: ∂y/∂t = −18·cos(2x−6t); ∂²y/∂t² = −108·sin(2x−6t) = −36y. Step 3: Check: ∂²y/∂x² = (1/v²)∂²y/∂t² → −4y = (1/v²)(−36y) → 1/v² = 4/36 = 1/9 → v = 3. Answer: It satisfies the equation with v = 3 units/s. Also v = ω/k = 6/2 = 3. ✓ Any function of (x − vt) passes this test.