Chapter 12: Waves in 1-D

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.