Video Transcript
Which word would correctly complete
the following statement about the resonant modes of electromagnetic waves in a
cavity? An electromagnetic wave that is a
resonant mode for a cavity must have blank displacement at the cavity
boundaries. (A) Zero, (B) nonzero, (C)
maximum.
Okay, so our statement is talking
about an electromagnetic wave that exists inside a cavity. A cavity is any bounded surface
with an interior. So, for example, this is a
cavity. Also, this is a cavity. Any closed surface with an interior
meets this condition. Inside a cavity then, it’s possible
for a wave to exist. But that can only happen under
certain conditions. The wave must satisfy what are
called the boundary conditions of the cavity. Simply put, for a wave to exist
between two points in a cavity wall, say, this point and this point here, that wave
must have a displacement of zero at both of these points.
For example, a wave like this,
where half a wavelength is between these two points, meets these boundary conditions
and therefore is a resonant mode for this cavity. A wave could also have this shape
and meet those boundary conditions and also this shape and so on. These are all resonant modes of
this cavity. And they all satisfy the boundary
conditions of having a displacement of zero at the cavity walls. Our completed statement reads “An
electromagnetic wave that is a resonant mode for a cavity must have zero
displacement at the cavity boundaries.”
