This lesson introduces you to the derivation of the 1D wave equation, which is one of the most important fundamental developments in the field of materials science. We also discuss what happens when waves encounter an "impedance boundary," or a boundary between two materials with different sets of dynamic properties. You will learn how propagating waves diverge, with a part that transmits into the new material and another part that reflects back into the original material. All of this content will set the stage for understanding how waves travel through soil, which we will cover in Part II of this series.