Question Detail
Question
Given that a wave is described by the equation y = sin 2(0.5t - x + π), calculate the particle velocity at (x, t) = (1, 3), where x and y are in meters and t in seconds.
Correct Answer
Option A is the correct answer.
Detailed Explanation
y = sin 2(0.5t - x + π) = sin(t - 2x + 2π). Particle velocity v_p = ∂y/∂t = cos(t - 2x + 2π) × 1 = cos(t - 2x + 2π). At (x, t) = (1, 3): v_p = cos(3 - 2 + 2π) = cos(1 + 2π) = cos(1) ≈ 0.5403. None of the options match. If the equation is y = sin(2(0.5t - x) + 2π) = sin(t - 2x + 2π), then v_p = cos(t - 2x + 2π). At (1, 3): cos(3 - 2 + 2π) = cos(1 + 2π) = cos(1) = 0.5403. The options are around 0.88. There might be a misprint.
Hint
Particle velocity is ∂y/∂t.