Particle Velocity and Wave Velocity Relation (v_particle = -v_wave × (∂y/∂x))
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v_particle = -v_wave × (∂y/∂x)
What each symbol means
| Symbol | What it stands for |
|---|---|
| v_p | Particle (transverse) velocity (m/s) |
| v_wave | Wave propagation velocity (m/s) |
| ∂y/∂x | Slope of wave at that point |
When to use this
Relates transverse particle velocity to slope of wave displacement. For y = a sin(kx - ωt): v_p = -aω cos(kx - ωt) and ∂y/∂x = ak cos(kx - ωt). Maximum particle velocity v_p_max = aω. Particle velocity and wave velocity are perpendicular for transverse waves.