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Question:

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

3π

23π

2π

32π

Solution:

The correct option is A
32π
From the wave equations, we know that
vmax = aω
v = nλ
vmax/v = aω/nλ = a(2πn)/nλ = 2πa/λ = 2πa/(2π/K) = Ka
a = π/2 × 3 = 3π/2