A simple harmonic wave of amplitude 2 mm is travelling along positive x-axis. At a given instant, displacements for two different particles on the wave are 1 mm and √2 mm along positive Y direction. If wavelength of the wave is 48 mm then find minimum separation between mean positions of the particles (in mm).
Physics · Mixed Chapter
JEE Mains

Question

A simple harmonic wave of amplitude 2 mm is travelling along positive x-axis. At a given instant, displacements for two different particles on the wave are 1 mm and √2 mm along positive Y direction. If wavelength of the wave is 48 mm then find minimum separation between mean positions of the particles (in mm).

Physics · Mixed Chapter

G1 Physics · Accepted Answer

Step 1: With y=A sinφ and A=2 mm, displacement y₁=1 mm corresponds to sinφ₁=1/2, so one possible phase is φ₁=π/6. Step 2: For y₂=√2 mm, sinφ₂=1/√2; a nearest compatible phase is φ₂=π/4. Step 3: Minimum phase difference is Δφ=π/4−π/6=π/12. Step 4: Spatial separation is Δx=λΔφ/(2π)=48/24=2 mm.