Last week was a relatively lousy one for me, but it was made up in part by getting a good question from a student on waves and interference after class. It’s really nice to get a question that indicates a genuine interest in the science (as opposed to just wanting an answer to homework), and I thought I’d discuss the question and its answer as a post.
The situation in question is as follows: suppose you have a harmonic wave on a string traveling to the right such that in a snapshot of time, the string looks as follows:
This wave carries energy, and there is a net flow of energy to the right. Now suppose we excite the string with an additional wave of the same frequency and amplitude, but completely out of phase. The sum of the two waves then vanishes:
The two waves cancel each other out, leaving a completely unmoving string due to destructive interference. My student asked me: what happens to the energy? As posed, it seems that we started with two waves carrying energy, but they canceled each other out, leaving no energy! This interpretation cannot possibly be correct, so where is the flaw in our description?



