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Displacement Relation for a Progressive #8211; (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 #8211; 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 = d<sup>2</sup> y/dt<sup>2</sup> Also, ⎜a<sub>max</sub>⎜ = #8211; ω<sup>2</sup> A
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