when we say that speed of a wave is u we mean that with respect to the medium the wave is travelling with a speed u . now consider a sine wave travelling in positive X direction on a string . all the particles of string (these are particles of medium ) will have different speeds . The wave has the same speed wrt all these particles and its speed is u (constant) . how is this possible ? let us say that a wave wave is propagating along +x axis with a speed u . all the particles have different speeds (along y axis wrt ground ) . let us say a particle p1 has a speed v1j (wrt ground); wave speed wrt this particle is ui which implies speed of wave wrt ground will be ui + v1j . another particle p2 has a speed v2j (wrt ground); wave speed wrt this particle is again ui which implies speed of wave wrt ground will be ui + v2j . this implies wave speed wrt ground will keep on changing ...... am i right ?