The following content is provided under a Creative
Commons license.
Your support will help MIT OpenCourseWare
continue to offer high quality educational resources for free.
To make a donation or view additional materials
from hundreds of MIT courses, visit MIT OpenCourseWare
at OCW.MIT.edu.
PROFESSOR: Visualization of standing waves
that are electromagnetic requires
that we see fields that are invisible and are
varying at a frequency higher than we can actually
perceive with our eyes.
The visualization of waves that are mechanical is easier.
Here, we've got a spring under tension.
The transfer's deflections satisfy the wave equation.
The object in this demonstration is
to see standing waves in the sinusoidal steady state.
Professor Zahn will provide a fixed termination at that end,
and I'll try and provide the sinusoidal exhortation.
First mode is pretty easy.
Here's the second mode, a little harder to do.
Try that again.
At any location, the response is sinusoidal.
We have a null in the middle, because a wave incident
on that termination comes back and interferes
with the incident wave.
Our objective here is to visualize
not a mechanical, but rather an electromagnetic standing wave.
Such a wave can be made to propagate
between parallel metal plates.
The electric field is directed from one plate to the other,
terminating in plus and minus surface charges
on the respective conductor surfaces.
The magnetic field is tangential to the conductors,
terminating in positive and negative axial surface currents
on the conductor surfaces.
Both E and H are perpendicular to the direction
of propagation.
We therefore have a transverse electromagnetic wave.
Such TEM waves can propagate on pairs of conductors
of arbitrary shape.
So we needn't be concerned with the width of the plates
relative to the spacing.
We're going to use a fluorescent lamp
to give a rough indication of the amplitude
of the electric field intensity.
The electric field created by the wave
will cause an ionization of the gas in the tube.
The resulting light is therefore an indication
of the distribution of the electric field intensity.
This field is oscillating at more than 100 megahertz.
So it's not possible for the eye to follow the oscillations.
It's the envelope of the field distribution that we'll see.
We can make standing waves by either short circuiting
or open circuiting the line.
Let's start with the plates shorted.
Here are the actual plates and the short.
They're driven at the left by a radiofrequency generator.
To see the lamp, we've turned the lights down.
Next, the generator is turned on and the lamp is put in place.
I'm rubbing my feet on the carpet
to generate static electricity to help ignite the lamp.
Remember, where there's light, there's
an oscillating electric field.
The dark areas are therefore where the electric field
tends to null.
At the right end, we also appear to have a null.
Remember, the right n is shorted.
We can see the nulls even better if the lights are turned out
completely.
The electric field intensity is shorted out
at the right termination.
Here's the theoretical field distribution.
The electric field amplitude is a maximum
a quarter wavelength from the short
and at intervals of a half wavelength
from that point to the left.
What we see is the magnitude or envelope of the standing
wave of electric field.
We can think of the electric field between the plates
as being analogous to the deflection of our spring.
The deflection, like the electric field,
is pinned to 0 at the right end.
The deflection, like both the electric and magnetic fields,
is an oscillating function of time.
It remains 0 at the null points.
The magnetic field amplitude is maximum
near the short and at multiples of a half wavelength
from the short.
Not only are the peaks in magnetic and electric field
displaced from each other spatially
by a quarter wavelength.
They're also 90 degrees out of phase in time.
So when the electric field is maximum,
the magnetic field is 0, and vice versa.
The energy shifts from electric to magnetic form
and back again in a 1/2 a cycle.
We could measure the magnetic field
with a one-turn induction coil.
The coil voltage displayed on the scope
indicates the magnetic field perpendicular to its axis.
First, we put the coil at the null in electric field.
The magnetic field is indeed tangential to the plates
and perpendicular to the direction of propagation.
The magnetic field should be a peak
here at the null in electric field.
Now, moving toward the short, where
the electric field is maximum, the magnetic field should null.
Then, at the short, it should peak again.
Note that the phase shifts by 180 degrees
as we pass through the null.
Standing waves also result if the plates are
open circuit at the right end.
Now, there can be no current in the y direction in the plates
at the end, and hence no tangential z
directed magnetic field between the plates there.
With the magnetic field 0 at the right termination,
the electric field there is a maximum.
It should peak at the termination
and at half wavelength intervals to the left of the termination.
Watch the peaks in intensity move
by a quarter wavelength as the short is removed.
Again, with the short on, and with the short removed.
It is the electric field intensity that is now
the maximum at the right end.
We see this better with the lights out.
By measuring the distance between nulls
in the electric field intensity, we
determine the half wavelength.
It appears to be about 70 centimeters.
Electromagnetic waves propagate on the line
at the velocity of light, C. So we
can deduce the frequency of the source driving
the plates at the left end.
The frequency is equal to the velocity
of light, 3 times 10 to the eighth meters
per second, divided by the wavelength, about 1.4 meters.
So the frequency must be about 210 megahertz.
This is the frequency that we should
deduce from the oscilloscope trace for the magnetic probe.
The period is about 5.2 nanoseconds, the frequencies
about 195 megahertz.
The agreement with the 210 megahertz
we found from the wavelength is consistent with the accuracy
of our measurements.
In visualizing electromagnetic standing waves,
we've used the light illumination
to indicate the electric field intensity and the probe
to measure the magnetic field intensity.
We've observed the distributions of E and H
with open and short circuit terminations.