Question

A plane wave ℰ = a cos (ωt — kx) propagates in a homogeneous elastic medium. For the moment t = 0 draw 

(a) the plots of ℰ, ∂ℰ/∂t, and ∂ℰ/∂x vs x; 

(b) the velocity direction of the particles of the medium at the points where ℰ = 0, for the cases of longitudinal and transverse waves; 

(c) the approximate plot of density distribution ρ (x) of the medium for the case of longitudinal waves.

Answer 1

(a) The given equation is,

Hence all the graphs are similar having different amplitudes.

(b) At the points, where ℰ = 0, the velocity direction is positive, i.e., along + ve x - axis in the case of longitudinal and + ve y- axis in the case of transverse waves, where dℰ/dt is positive and vice versa.