Question

What is Displacement Relation for a Progressive Waves?

Answer

Displacement Relation for a Progressive Waves - (i) If a plane wave travels in a medium along the position x-direction, then the displacement y of a particle located at x at time t is given by y(x,t) = Asin(ωt - kx) where, A = Amplitude of the wave ω = 2π/T or 2πv is angular frequency k = (2π/λ), i.e. angular wave number, (ii) If a wave is travelling along the negative x-direction, then y(x,t) = A sin (ωt + kx), (iii) A particle velocity at a given position at a given time is equal to product of wave velocity and negative of slope of the wave curve at the given position and time. v-particle = -v(∂y/∂x), (iv) Acceleration of a particle at (x,t) is a = d² y/dt² Also, ⎜a_max⎜ = - ω² A