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Question Video: Choosing Possible Resonant Modes of a Cavity Physics • 9th Grade

Which of the electromagnetic waves shown in the diagram of a cavity corresponds to a possible resonant mode of the cavity?

02:02

Video Transcript

Which of the electromagnetic waves shown in the diagram of a cavity corresponds to a possible resonant mode of the cavity?

In these three options, we see three different waves inside of our cavity represented by the black box. We want to identify which one corresponds to a possible resonant mode of the cavity. A resonant mode of the cavity means we’re talking about an electromagnetic wave that satisfies what are called the boundary conditions of the cavity. Any cavity, any shape, has boundary conditions. Say that we had a cavity with this shape, and we wanted to set up an electromagnetic wave between, say, this point and this point in the cavity walls.

The requirement for that, the boundary condition, is that the displacement of whatever wave exists between these two points at those points in the wall is zero. So, for example, because a wave like this satisfies the conditions of having a displacement of zero at the two walls, this is a possible resonant mode of the cavity. And there are other waves possible between these two points that satisfy those same boundary conditions. For example, a wave like this meets those conditions of having a displacement of zero at the walls, and so does this one and so on.

In looking over our answer options then, we’ll be looking for a wave that satisfies the boundary condition that its displacement is zero at the two points where it meets the cavity wall. In option (A), those two points are here and here. We see that the wave’s displacement at the first of those points is zero. But that’s not true at the second point. Because this wave does not meet the boundary conditions of the cavity, it cannot be a possible resonant mode.

In answer option (B), the two points where the wave meets the wall are here and here at the ends of the dashed line. And once again, the displacement of the wave at the first point is zero, but not at the second point. This wave too fails to meet the cavity’s boundary conditions. In option (C) though, at the ends of the dashed line where the wave interacts with the cavity wall, we see the wave’s displacement at both of these points is zero.

Our answer then is option (C). The wave shown in this choice does correspond to a possible resonant mode of the cavity.

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