A
Stretch the
Slinky® between two people.
Or,
tie one end of the Slinky® to a chair or other solid object the same distance
away.
To
Do and observe
Move
your hand up and down, record observations..
What
is moving along the Slinky®?
The up down motion moves along the Slinky®.
This wave is a movement of motion! This wave is called a transverse wave
because the motion of the Slinky® is sideways to the motion along the Slinky®.
It provides a model for waves moving along strings, for light waves(in
particular linearly polarized light waves, and for seismic waves called S
waves.
You may also move your hand side to side to send horizontally
polarized waves.
Move
your hand side to side and up and down at the same time so that it moves in a
circle. A rotational wave moves down the Slinky®. This models circularly
polarized light. There are two possible directions to move your hand in the
circle, clockwise and counter-clockwise.
Move
your hand toward and away from you. record observations..
This
wave is a wave of motion back and forth along the Slinky® which travels along
the Slinky®, because the back and forth motion is in the same line as the
direction of motion this is called a longitudinal wave. The longitudinal wave
is a model for sound waves in gases and liquids as well as for seismic P waves.
This type of wave is also called a compression wave.
Move
your hand toward and away from you at the same time that you move it up and
down so that it makes a circular motion. record observations..
A
circular motion wave moves along the Slinky®. This models ocean waves and a
type of earthquake wave called a love wave. However, whereas the transverse and
longitudinal waves described first moved through the bulk of a material, the
ocean wave and the love wave are surface phenomena. Their motions are greatest
at a surface and decrease with depth.
Move
your hand side-to-side as well as toward and away to make a circle in a
horizontal plane. A wave of this motion will not travel in liquids and gases
but it will travel in solids like the earth and this Slinky®. This models a
seismic wave known as a Rayleigh wave.
Rotate
your wrist. record observations. This is a torsional wave.
When
a bow is drawn across a violin string the string twists and a torsional waves
travels down the string.
What’s
Going On?
All
waves involve restoring forces, forces which tend to restore a deformation to
its original shape. Push a few atoms in a solid in any direction and forces
will push them back towards their original position. Push some atoms in a gas
or liquid to the side however and they will stay there. Without restoring
forces waves cannot propagate, so transverse waves do not move through gasses
and liquids.
Try
to make a denser region in a gas or a liquid and forces will oppose you, When
you make a longitudinal or compression wave, you make regions of high and low
density. So that there are restoring forces and longitudinal waves can go
through liquids and gases.
Etc
Transverse seismic waves cannot pass through the outer
core of the earth while longitudinal seismic waves can, thus the outer core of
the earth must be a liquid.
To
Do and Notice
Hold
the Slinky® between your hands. The Slinky® will be horizontal and sag. Move
both of your hands up-and down together. Find the lowest frequency which
produces the largest motion of the Slinky® for the smallest motion of your
hands. (About one cycle per second.) One large hump, half-a-wave should appear
moving up and down on the Slinky®.
Count
the rhythm, 1,2,3,4,1,2,3,4,...
Move
your hands in opposite directions, the right hand up when the left hand moves
down and vice-versa. Move them in the same rhythm as above. Notice that your
hands move a large distance. The center of the Slinky® does not move
up-and-down at all.
What
is Going On?
When
you move your hands together you get a half-a-wave on the Slinky® the middle of
the Slinky® is an antinode, the hand-held ends are nearly nodes.
When
you move your hands opposite, a half-a-wave also fits on the Slinky®. However,
this half wave has one node in the center and two antinodes near the hand-held
ends.
The
timing on both of these is the same. They both are one-half-wave resonances
ETC.
For
the transverse motion of the Slinky®, pressure is modeled by the slope of the
Slinky®. At places where the motion of the Slinky® passes through zero, a node
of motion, the slope of the Slinky® changes the most, an antinode of slope.
Longitudinal
Waves
To
Do and Notice
Grab
the ends of the Slinky® in your hands. Stretch the Slinky® to between 1 and 2
meters long.
Move
your hands together and then apart, just as if you were clapping. Notice the
motion of the Slinky®. Your hands move a lot while the center of the Slinky®
moves very little. The center is a node.
Next,
notice the spacing between the slinks (turns) of the Slinky®. When the slinks
are jammed close together the Slinky® models high pressures in a gas where the
atoms are closer together. When the slinks are far apart, the Slinky® models
low pressure gas. Let’s call closely spaced slinks high pressure and widely
spaced slinks low pressure. Notice that the pressure change is greatest at the
center where the slinks alternately bunch-up and spread apart. Count the rhythm
of this motion: 1,2,3,4,1,2,3,4,...
Move
both hands in the same direction, if the Slinky® stretches right-left move both
hands to the left then to the right. (One of our teachers described this as the
buhdist clap, two one handed claps!)
Notice
the motion of the Slinky® which is called longitudinal motion. Find the
frequency of hand motion that produces the largest motion of the center of the
Slinky® for the smallest motion of your hands. Count the rhythm of this motion:
1,2,3,4,1,2,3,4,...
Notice that the center of the Slinky® is an antinode,
your hands are nearly nodes. Notice that in the center the Slinky® moves back
and forth but the spacing between the slinks near the center does not change.
The center is an antinode of motion but a node ( a place with no change) of
pressure. At the nodes of motion near your hands, however the slinks bunch
together and then spread apart: the pressure changes a lot. The hand-held ends
are antinodes of pressure. Notice also that when one hand is at high pressure
the other is low. The ends then swap the high pressure one becomes a low
pressure and vice-versa. In other words, the slinks bunch up near one hand
while they spread out at the other.
What
is Going On?
When
your hands move together one-half-wave of longitudinal motion fits on the
Slinky®. This is the lowest frequency resonance of the Slinky® and it has what
is called the fundamental frequency.
When
your hands move opposite, one-half-wave of longitudinal motion also fits on the
Slinky® but this time the node is in the middle while your hands are near
antinodes.
A
sound wave is a longitudinal wave. A sound wave can be viewed either as a wave
of motion of atoms or as a wave of pressure. In a standing sound wave nodes of
motion occur at the same place as antinodes of pressure.
To
Do and Notice
Find
a higher frequency resonance of the longitudinal wave in which you move both
hands in the same direction. You should have to move your hands about twice as
often as in the lowest frequency resonance you created before.
Count
the frequency: 1,2,3,4,1,2,3,4 Notice the motion of the Slinky®, there are two
nodes each about 1/4 of the way from each end.
One full wave fits on the
Slinky®. When there is a high pressure near one node there is low pressure near
the other. The high pressure and low-pressure regions switch positions each
cycle.
Move
your hands opposite each other and find the next higher resonant frequency.
There
will be three nodes on the Slinky®, one in the center and the other two1/6 of
the Slinky® from each end.
3/2 of a wave fits on the Slinky®. Notice the
pressure changes on the Slinky®, when one node is experiencing high pressure
the adjacent one experiences low pressure. With time, each node oscillates from
high pressure to low and back again.
What
is Going On?
High
pressure and low-pressure nodes alternate in time as well as in space. To
create an odd number of nodes move your hands opposite each other, clap hands.
To create an even number of nodes move your hands in the same direction.
Do
pulses bounce off each other or pass through? Design, conduct, and describe specifically the experiment you did to prove
your conclusion.
------------------------------------------
B
Method:
1)
Stretch the Slinky® out on the floor approximately 3 meters with one person
sitting down
holding
onto to each free end. One of the holders should transmit a transverse pulse by
rapidly
moving
the end of the Slinky® ON THE FLOOR from side to side. The pulse should be
formed
by
moving the Slinky® rapidly out to the right of the person forming the pulse and
back to the
starting
point. This will be called a ‘right’ pulse.
Describe what happens when the pulse
reaches the far end (this is called a closed
reflection).
Does it come back as a ‘right’ or ‘left’ pulse?
2)
Stretch the Slinky® out on the floor approximately 3 meters with one person
sitting down
holding
onto to each free end. Have the person with the string end hold the Slinky® by
pulling
lightly
on the string. The OTHER holder
should transmit a transverse pulse by rapidly moving
the
end of the Slinky® ON THE FLOOR from side to side. The pulse should be formed by
moving
the Slinky® rapidly out to the right of the person forming the pulse and back
to the
starting
point. This will be called a
‘right’ pulse.
Describe what happens when the pulse
reaches the far end (this is called an open
reflection). Does it come back as a ‘right’ or
‘left’ pulse?
Description:
3)
Stretch the Slinky® out on the floor approximately 3 meters with one person
sitting down
holding
onto to each free end. Both
holders should transmit a transverse pulse by rapidly
moving
the end of the Slinky® ON THE FLOOR from side to side. The pulse should be formed
by
moving the Slinky® rapidly out to the same side (one person’s right and the
other’s left) and
back
to the starting point.
Describe what happens when the two
pulses meet in the middle (This is called
constructive
interference). Do they make a
larger or smaller pulse at the moment of meeting?
Note:
it is some times easier to see by tying a small ribbon exactly in the middle an
observing
how
the ribbon moves (or doesn’t move) when the pulses meet.
Description:
4)
Stretch the Slinky® out on the floor approximately 3 meters with one person
sitting down
holding
onto to each free end. Both
holders should transmit a transverse pulse by rapidly
moving
the end of the Slinky® ON THE FLOOR from side to side. The pulse should be formed
by
moving the Slinky® rapidly out to OPPOSITE sides (one person’s right and the
other’s right)
and
back to the starting point.
Describe what happens when the two
pulses meet in the middle (This is called destructive
interference). Do they make a larger or
smaller pulse at the moment of meeting? Note: it is
some
times easier to see by tying a small ribbon exactly in the middle an observing
how the
ribbon
moves (or doesn’t move) when the pulses meet.
Description:
5)
Stretch the Slinky® out on the floor approximately 3 meters with one person
sitting down
holding
onto to each free end. One of the
holders should transmit a continuous set of transverse
pulses
by rapidly moving the end of the Slinky® ON THE FLOOR from side to side and
continuing
the movement. The wave should be
formed by moving the end of the Slinky® back
and
forth rapidly. The waveform
desired will have a single “hump” which moves out to the right
and
then out the left. Some adjustment
in timing will be necessary until the wave is formed.
This
is called a standing wave and also a fundamental.
Describe the number of points on the
wave that move the maximum distance (antinodes).
Describe
the number of points on the wave that do not move at all (nodes). Describe the
wavelength
of the fundamental in terms of the distance between the two ends of the
Slinky®.
6)
Stretch the Slinky® out on the floor approximately 3 meters with one person
sitting down
holding
onto to each free end. One of the
holders should transmit a continuous set of transverse
pulses
by rapidly moving the end of the Slinky® ON THE FLOOR from side to side and
continuing
the movement. The wave should be
formed by moving the end of the Slinky® back
and
forth rapidly. The waveform
desired will have two “humps” which move out to the right
and
then out the left. Some adjustment
in timing will be necessary until the wave is formed.
This
is called a standing wave and also a second harmonic.
Describe the number of points on the
wave that move the maximum distance (antinodes).
Describe
the number of points on the wave that do not move at all (nodes). Describe the
wavelength
of the second harmonic in terms of the distance between the two ends of the
Slinky®.
Description:
7)
Stretch the Slinky® out on the floor approximately 3 meters with one person
sitting down
holding
onto to each free end. One of the
holders should transmit a continuous set of transverse
pulses
by rapidly moving the end of the Slinky® ON THE FLOOR from side to side and
continuing
the movement. The wave should be
formed by moving the end of the Slinky® back
and
forth rapidly. The waveform
desired will have three “humps” which move out to the right
and
then out the left. Some adjustment
in timing will be necessary until the wave is formed.
This
is called a standing wave and also a third harmonic.
Describe the number of points on the
wave that move the maximum distance (antinodes).
Describe
the number of points on the wave that do not move at all (nodes). Describe the
wavelength
of the third harmonic in terms of the distance between the two ends of the
Slinky®.
Description:
8) Given the pattern for the above three
activities, describe the
a) number of nodes for the nth harmonic
b) number of antinodes for the nth
harmonic
c) wavelength of the nth harmonic in terms
of L (the distance between the two ends
of
the Slinky®)
Description:
9)
Tie the Slinky® with the other long coil of wire. Stretch the combined Slinky® out on the
floor
approximately 6 meters with one person sitting down holding onto to each free
end. One of
the
holders should transmit a transverse pulse by rapidly moving the end of the
Slinky® ON
THE
FLOOR from side to side. The pulse
should be formed by moving the Slinky® rapidly out
to
the right and back to the starting point.
This will be called a ‘right’ pulse.
Describe
what happens when the pulse encounters the boundary between the two coils
(this
is called refraction and reflection).
Note: Two pulses should be observed!
Description:
10)
Tie the Slinky® with the other long coil of wire. Stretch the combined Slinky® out on the
floor
approximately 6 meters with one person sitting down holding onto to each free
end. One of
the
holders should transmit a longitudinal pulse of the Slinky® ON THE FLOOR. The pulse
should
be formed by gathering some Slinky® coils at one and then suddenly releasing
them.
This
will be called a longitudinal pulse.
Describe
what happens when the pulse encounters the boundary between the two coils
(this
is called refraction and reflection).
Note: Two pulses should be observed!
Description:
11)
Stretch the Slinky® out on the floor approximately 3 meters with one person
sitting down
holding
onto to each free end. One of the
holders should transmit a transverse pulse by rapidly
moving
the end of the Slinky® ON THE FLOOR from side to side. The pulse should be formed
by
moving the Slinky® rapidly out to the right of the person forming the pulse and
back to the
starting
point. Using the stopwatch,
determine the time for a single pulse to travel from the
originating
end, down to the other end and return back to the originating end. Repeat this twice
more
and get an average time. Measure
the length of stretch and determine the velocity. Repeat
this
experiment for 3.5 m, 4 m, 4.5 m and 5 m.
Graph
the velocity versus the length.
Determine a relationship between the length of Slinky®
and
the velocity of the wave.
TAKE DATA and observations ON THE FOLLOWING FOR A TRANSVERSE WAVE WITH A COILED SPRING
(one or two pulses is preferable)
You need stopwatches, metersticks and good eyes.
The effect of amplitude on the speed of the wave.
The effect of amplitude on the frequency and wavelength of
the wave.
The effect of amplitude on one point on the wave (mark
with tape or paper).
The effect of tension on the speed, frequency, wavelength
and one point on the wave
