I want to verify my understanding of D'Alembert equation. Please let me know my statements are correct or not.

D'Alembert equation:

1) represent wavepropagateright and left on the x-axis with velocity ofc.

2) g(x) is velocity along y-axis, not in direction of x-axis. g(x)DO NOTaffect the propagation velocityc.g(x) only affect the shape of the wave while propagating along x-axis.