A simple harmonic wave is y = 3 sin[(π/2)(50t - x)], where x and y are in metres and t in seconds. Find the ratio of maximum particle speed to wave speed.
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A simple harmonic wave is y = 3 sin[(π/2)(50t − x)], where x and y are in metres and t in seconds. Find the ratio of maximum particle speed to wave speed.

G1 Physics · Accepted Answer

Step 1: y = 3 sin[(π/2)(50t − x)] gives ω = 25π s⁻¹, k = π/2 m⁻¹ and wave speed v = ω/k = 50 m s⁻¹. Step 2: Maximum particle speed is Aω = 3×25π = 75π m s⁻¹. Ratio = 75π/50 = 3π/2. Final: D.