Practice portal › Waves › Progressive Waves and the Displacement Relation

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

Asked in NEET 2012 Mains · Particle velocity and wave velocity

Answer: (2) 3/2π

Step-by-step solution

Given: y=3 sin π/2(50t-x).

Expanding, y=3 sin (25π t-π/2x), so A=3, ω=25π, k=π/2.

Wave velocity: v=ω/k=(25π)/(π/2)=50 m s⁻¹.

Maximum particle velocity: (vₚ)ₘₐₓ=Aω=3×25π=75π m s⁻¹.

((vₚ)ₘₐₓ)/v=(Aω)/(ω/k)=Ak.

Ak=3×π/2=3/2π.

Why the other options are wrong

More Progressive Waves and the Displacement Relation questionsAll Progressive Waves and the Displacement Relation questions →

Reading this solution needs no sign-in. You only sign in to practise against the clock and keep your progress.

Practise this with a timer