Wave Motion: Why Does Particle Lag Behind its Predecessor?

[sunmoon]

For an progressive wave why the phase particle lags behind of time than it's predecessor one ? we know for a particle which is at the origin follows the equation # # y=# # A sin \omega t and the following particle follows # # y=# # A sin \omega (t-x/t)

 

[sophiecentaur]

Hi and welcome.
I asked that very same question when I was at school; it seems 'backward' at first sight. The Maths describes what happens and you can justify that negative sign in the wave equation by realising that the phase of the wave, seen at a more distant point, is earlier (because the later bit of the wave hasn't arrived yet). The negative phase value means a lag in the wave.