Notes

Displacement Relation for a Progressive Waves …

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