Video Transcript
Which of the electromagnetic waves shown in the diagram of a cavity corresponds to a possible resonant mode of the cavity?
Let’s start by recalling what a resonant mode of a cavity is. Say that over here we have a cavity, and it could be any shape. It’s possible for waves, say, waves of light or waves of sound depending on the size of the cavity, to exist between two points in the cavity wall. But there’s a condition for this. Any wave that exists in the cavity needs to meet what are called boundary conditions. In this case, those conditions are that any place the wave meets the cavity wall, the wave must have a displacement of zero. That means, for example, that the wave we’ve drawn here has the longest possible wavelength for any wave that could exist between these two points in the cavity wall.
However, it is possible for a shorter wave to exist between these two points. Here is a wave whose entire wavelength fits between these two points. But notice that it still has to satisfy the boundary conditions having a displacement of zero where it meets the wall. That’s the condition of a resonant mode in a cavity.
Considering then our two answer choices (A) and (B), we see that the wave in answer option (A) begins at this point on the wall and ends at this point. At both locations, its displacement is zero. The wave in option (B) though begins at this point on the wall and ends purportedly here. However, when the wave meets the cavity wall on the right, its displacement we can see is not zero. Therefore, it does not satisfy the required boundary conditions. And that means that this wave as drawn can’t exist between these two points in our cavity. Therefore, the wave shown in option (A) is the only wave that corresponds to a possible resonant mode of the cavity.
