Animation 1
Translation of a Function
A function of a single, real variable is translated to the right on the abscissa if we subtract a positive number from its argument. The amount of translation is equal to this subtracted number:

If a positive number is added to the argument, the function would translate to the left.
One-dimensional (1-D) Waves
The 1-D wave equation
has its general solutions in the forms
with v being the velocity of propagation of the wave.
Observe the 1-D Gaussian-pulse as an incident (left plot) and reflected (right plot) waves.
 

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