Radio Waves & Electromagnetic Fields SIM Homework Answer Key

rawfrogpondUrban and Civil

Nov 16, 2013 (3 years and 4 months ago)

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Radio Waves
&

Electromagnetic

Fields
SIM

Homework

Answer Key

1
) For this question, use the
Radio
Waves
&

Electromagnetic Fields
s
imulation

to
guide your understanding of how Radio broadcasting and Radio receivers work.
This simulation is available at the P
hysics 1010 Homepage.

a)

How is the radiating electric field (or electromagnetic signal) produced when radio
stations broadcast? Include a description of what is producing the signal as well as the
reasoning behind how this could produce a signal.

Electro
magnetic radiation is produced by accelerating charges. In the
radio transmitter, electrons oscillate up and down and are thus
accelerating. An electron will exert a force on another electron when
they are some distance away, like charges repel. When the e
lectron in
the transmitter oscillates up and down, the direction of the force it
exerts changes since the source of the force (the oscillating electron) is
moving. It takes some time for the change in this direction of the force
to be felt since this chang
e is communicated or propagated out at the
speed of light. In addition, the horizontal component of this force is
canceled by the positive charges in the transmitting antenna. So, the
resulting force is an oscillating force that pushes vertically on electr
ons.
This force propagates out as a wave as the signal travels at the speed of
light.

b)

How does your antenna work to detect this electromagnetic signal produced when
radio stations broadcast? Include the physics principles that support your description
o
f how this signal is detected.

Electromagnetic radiation is a form of energy that exerts a steadily
oscillating force on charges (electrons)... first the force will be exerted
strongly in one direction then this will reverse and the electron will feel a
s
trong force in the opposite direction, and the cycle will continue. In the
radio antenna, the radio

waves passing by push on the electrons in the
metal in the antenna and cause them to oscillate up and down the length
of the antenna. This creates a current

in the antenna.

2) Using the s
imulation, adjust the transmitter so that it is in sinusoidal mode and
the electrons are oscillating up and down at a regular frequency. This is how radio
waves are broadcast. Set it so that both “display the curve” and the
“radiated field”
boxes are checked.

a)

What does the curve represent?

The line of electrons being sprayed off of the antenna that then cause the receiver
electron to move.

The pat
h that an electron will follow due to the electromagnetic wave.

The evenly spaced electrons moving up and down between the two antennae.

The field of negative charges that are movi
ng through space.

The strength and direction of the force that would be exerted by the
electromagnetic wave on an electron
.

b)

With the frequency set at the mid
-
point of the slider and the amplitude set at the
mid
-
poi
nt of the slider, approximately how many grid marks is the wavelength of the
wave (use the pause button and step button as you need to in order to get a good
measure, and round to the nearest whole grid mark)?

The wavelength of the wave the distance betwe
en the peak of one wave
and the peak of the next, between the minimum of one and the minimum
or the next, or between any two points the encompass one complete wave
cycle. Equivalently, this is the distance the wave travels from when say
the electron is at
the peak of its motion and the next time it gets to the
peak of its motion. Either way this is about 10 or so grid points.

If the amplitude is increased, the wavelength

decreases


increases


stays the same



The amplitude affects the strength of the force ... that is the length of
the force vectors in the electromagnetic wave. The wavelength of the
wave depends only on the frequency with whic
h the electron in the
transmitting antenna is oscillating up and down; and the speed of light.

Wavelength x Frequency = Speed of Light

c)

Use the simulation to evaluate the following statements.

True


False


If the oscillation frequency of the transmitting electron
decreases, the oscillation frequency of the electron in the receiver is
instantaneously

affected.

The electron in the receiving antenna feels only the force resulting
from
the electromagnetic wave at its current location. It only "sees" the
transmitting electron because of the effects that the transmitting
electron has on the electromagnetic waves. So the receiving electron will
keep oscillating at its original frequenc
y until the electromagnetic waves
with the new frequency arrive. (they move towards the receiving antenna
at the speed of light).

True


False


The electron in the receiving antenn
a oscillates at a lower
frequency than the electron in the transmitting antenna because of the distance
between the antennas.

When the electron in the transmitting antenna oscillates, it sets up an
electromagnetic wave oscillating at the same frequency. T
his
electromagnetic wave in turn causes the electron in the receiving antenna
to oscillate at the same frequency. So the electrons in the transmitting
and receiving antennas must oscillate at the same frequencies.

True



False


If the frequency of oscillation increases but the amplitude of
the electron oscillation remains the same, then the electron in the transmitting antenna
is experiencing larger accelerations (recall what you kn
ow about acceleration and
motion).

In order for the frequency to increase but the amplitude to stay the
same, the electrons must be moving faster as they oscillate back and
forth. A measure of the average acceleration is the (change in
velocity)/(time elap
sed). If the electron is moving faster towards its
peak height and then away from its peak height at this new frequency, it
has experience a larger change in velocity than at the old frequency. In
addition, the time elapsed for this change in velocity is l
ess than for the
old frequency. Both changes indicate that the acceleration must be
larger.

True



False

If the amplitude increases but frequency remains the same, the
electron a
t the receiving antenna experiences larger peak forces but oscillates at the
same frequency as before.

The larger the acceleration of the transmitting electron, the stronger
the electromagnetic radiation emitted, that is, larger force vectors.
When the am
plitude of the transmitting electron increase, the electron
in the transmitting antenna is experiencing larger accelerations so the
magnitude (strength) of the electromagnetic radiation (the force on the
electron) produced is larger. Thus, the force on the

electron results from
the
strength

of the electromagnetic wave. The frequency of the wave
determines how quickly the electron switches directions (oscillates).

True


False


If th
e frequency of the transmitting electron decreases by a
factor of two, it will now take longer for the electromagnetic signal to reach the
receiving antenna.

Electromagnetic waves travel at the speed of light, which is a constant.

True


False


If the frequency decreases, the wavelength decreases.

Wavelength and frequency are related by frequency*wavelength = speed
of light, or wavelength = c/frequency. c is the speed of light. So

if
frequency decreases, the wavelength increases.

True



False

The electromagnetic waves generated by the transmitting
antenna produce currents in the receiving antenna.

The elec
trons in the receiving antenna move up and down in response to
the forces put on them by the electromagnetic waves. Since a current
consists of charges moving, this will result in a current being detected in
the receiving antenna
.

True


False


When the electron in the transmitting antenna is at its peak
height, the electron in the receiving antenna is always also at its peak height.

First, we can see this is not true by playing wit
h the simulation. For a
subtler explanation, imagine if we had two receiving antennas, placed a
distance away from each other which was equal to half of the wavelength
of the electromagnetic waves. Then whenever the electrons in the first
antenna were bein
g pushed upwards, the electrons in the second antenna
would be pushed downward. So if the electrons in the first antenna were
at their peak height at the same time as the electrons in the transmitting
antenna, the electrons in the second antenna would be a
t their
lowest

height. So the answer has to be false.

Explain your reasoning to your answer for the T/F If the frequency of oscillation
increases but the amplitude of the electron oscillation remains the same, then the
electron in the transmitting antenna
is experiencing larger accelerations (recall what
you know about acceleration and motion). Include in your explanation how this
affects the strength of the transmitted electromagnetic signal (revisit the simulation if
you did not notice what happened to th
e strength of the transmitted signal).

In order for the frequency to increase but the amplitude to stay the
same, the electrons in the transmitting antenna must be moving faster as
they oscillate back and forth. A measure of the average acceleration is
th
e (change in velocity)/(time elapsed). If the electron is moving faster
towards its peak height and then away from its peak height at this new
frequency, it has experienced a larger change in velocity than at the old
frequency. In addition, the time elapse
d for this change in velocity is less
than for the old frequency. Both changes indicate that the acceleration
must be larger.

When the transmitting electron experiences larger accelerations, the
strength of the transmitted electromagnetic signal is larger.


d)

For the radio wave transmitter in the simulation, which of the following
orientations of the receiver antenna will pick up the signal? (Select all that will)

an antenna oriented vertically

an antenna oriented horizontally (parallel to the ground) with one tip pointing
towards the transmitting antenna (so it is oriented East
-
West)

an antenna oriented horizontally and perpendicular to t
he antenna in the previous
answer (so it is oriented North
-
South)

Antennas work best when they are parallel with the transmitting antenna
so that the forces from the electromagnetic wave act to push the
electrons back and forth along the length of receivin
g antenna. When the
receiving antenna is perpendicular to the transmitter, the force from the
electromagnetic wave does not act to push the electrons back and forth
along the length of the antenna, so no current will flow. The electrons will
feel a force a
long the small radius of the rod.

e)

Which one of the following sets of graphs of position vs. time, velocity vs. time,
and acceleration vs. time corresponds with the motion of the electron in the receiving
antenna? (It may help to remember the relationsh
ip between force and acceleration,
and use the “Step” feature to step through the motion of the electron and have the
vectors display the “force on an electron”.)



The correct graph is

F

The position, velocity and acceleration all oscillate smoothl
y, so a and b
can't be correct. But how do we choose between the other graphs?

1)When the electron is as far up or down as it can possibly go, its velocity
must be zero.

2)When the electron is as far down as it can go, its acceleration must be
upwards (and

vice versa). We know this because, while the velocity is
instantaneously zero, it will soon be positive, so that acceleration must be
positive.

Putting these two together, the only graph which fits both criteria is F.