Q. The equation of a simple harmonic wave is given by y = 3 sin (π/2)(50t − x), where x and y are in metres and t is in seconds. The ratio of maximum particle velocity to the wave velocity is
A) 2π
B) (3/2)π
C) 3π
D) (2/3)π
Explanation
[Solution from source] y = 3 sin(25πt − πx/2), so A = 3 m, ω = 25π rad/s, k = π/2 m⁻¹. Wave speed = ω/k = 50 m/s and maximum particle speed = Aω = 75π m/s, giving a ratio of 75π/50 = 3π/2. Answer (2).
Reviewed by Dr. Abubacker
Physics Educator & NEET/JEE Specialist
Ph.D. in Physics with 19+ years of teaching experience.