A typical introduction to electromagnetic waves in vacuum is illustrated by the following quote from an introductory physics text: "Maxwell's equations predict that an electromagnetic wave consists of oscillating electric and magnetic fields. The changing fields induce each other, which maintains the propagation of the wave; a changing electric field induces a magnetic field, and a changing magnetic field induces an electric field." Students' intuition, developed from repeatedly solving simple problems involving Faraday's law in an introductory physics course, can lead them to expect the electric and magnetic waves to be out of phase, in contradiction to physical reality as described by Maxwell's equations. Below, we present the type of common Faraday's law problem that promotes this cognitive pitfall, and we suggest an approach that we believe leads to a deeper, more correct student understanding of electromagnetic waves.