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The equation of a simple harmonic wave is given by y = 3 sin(π/2 (50 − x)). Where x and y are in meters and t is in seconds. The ratio of maximum particle velocity to the wave velocity is:

1. 2π
2. 3π/2
3. 3π
4. 2π/3

Correct answer: 3π

Solution

The maximum particle velocity is given by ωA, where ω is the angular frequency and A is the amplitude. From the equation, ω = π/2 and A = 3. The wave velocity is given by v = ω/k, where k = π/2. Thus, the ratio of maximum particle velocity to wave velocity is (ωA) / (ω/k) = A * k = 3 * π = 3π.

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