Post­Lab Slinky.notebook
February 08, 2013
Longitudinal Pulse
Post­Lab Slinky.notebook
Once again its Slinky Time
February 08, 2013
Post­Lab Slinky.notebook
February 08, 2013
Longitudinal Waves: Instead of moving up and down, the wave moves forward and backward along the direction of the wave.
What is the wavelength (λ) of a longitudinal wave?
This is how sound waves work, but that's next chapter!!!
Post­Lab Slinky.notebook
February 08, 2013
Longitudinal Waves: Instead of moving up and down, the wave moves forward and backward along the direction of the wave.
Wavelength
What is the wavelength (λ) of a longitudinal wave?
This is how sound waves work, but that's next chapter!!!
Post­Lab Slinky.notebook
February 08, 2013
Longitudinal
(This is how you draw them)
vs.
Transverse
Post­Lab Slinky.notebook
February 08, 2013
Longitudinal
(This is how you will see them)
vs.
Transverse
Post­Lab Slinky.notebook
February 08, 2013
Longitudinal
vs.
Transverse
The dark bars correspond to COMPRESSIONS. They are analogous COMPRESSIONS
to transverse 'CRESTS'
Post­Lab Slinky.notebook
February 08, 2013
Longitudinal
vs.
Transverse
The dark bars correspond to COMPRESSIONS. They are analogous COMPRESSIONS
to transverse 'CRESTS'
The light bars correspond to RAREFACTIONS. They are analogous to RAREFACTIONS
transverse 'TROUGHS'
Post­Lab Slinky.notebook
February 08, 2013
Post­Lab Slinky.notebook
February 08, 2013
Longitudinal Wave: the pulse causes a disturbance in the direction of the wave.
Transverse Wave:
the pulse causes a disturbance perpendicular to the direction of the wave.
Post­Lab Slinky.notebook
February 08, 2013
WATER WAVES ARE BOTH!
Post­Lab Slinky.notebook
The FUNdamental wave:
February 08, 2013
Post­Lab Slinky.notebook
February 08, 2013
= NODE
= ANTINODE
Post­Lab Slinky.notebook
February 08, 2013
What's a Harmonic?
Fundamental/First Harmonic
Second Harmonic
Third Harmonic
Post­Lab Slinky.notebook
February 08, 2013
What's a Standing
Wave?
Post­Lab Slinky.notebook
February 08, 2013
What's a Standing
Wave?
A standing wave is a waveform where the nodes don't move. Thanks Slinky!!!
Post­Lab Slinky.notebook
February 08, 2013
Procedure:
1. Stretch the slinky out on the floor approximately 5 meters with one person sitting down holding onto to each free end. With a quick sideways flick of the wrist, you should be able to generate a single, easily observed pulse. This is a ‘transverse’ pulse.
Look at the pulse as it moves along the slinky.
Does its shape change? ____ Does its speed change?____
Transverse Pulse
Post­Lab Slinky.notebook
February 08, 2013
2. With a quick ‘push’ of the slinky, you generate a wave pulse the goes straight through the slinky (no sideways ‘hump’). Do this a few times until you can see the pulse travel through the slinky and reflect back. This is called a ‘longitudinal’ pulse.
Does its shape change? ____ Does its speed change? ____
Longitudinal Pulse
Post­Lab Slinky.notebook
February 08, 2013
3. Get your slinky lined up next to another group’s slinky. Make sure you leave at least a meter between them so they don’t tangle. Make sure the slinkies are stretched to the same length (about 5 meters).
Generate a large pulse in one slinky and a small pulse in the other slinky at the same time. Does the speed of the pulse depend on the size of the pulse?
Post­Lab Slinky.notebook
February 08, 2013
4. Still matching up with another group: Increase the tension in one slinky by gathering up 15­20 coils of the slinky on one end, making sure the slinkies are still stretched to the same length. Generate a pulse in each slinky simultaneously. Does tension affect the speed of the pulse? _______ If yes, how (does more tension increase or
decrease the speed)?
WAVE SIMULATION TIME!!!
Post­Lab Slinky.notebook
February 08, 2013
5. Leave the other team and go back on your own: One of the holders should transmit a single transverse pulse to the right while the other person holds their end still (hold the slinky, not the string). This will be called a 'right' pulse.
Describe what happens when the pulse reaches the far end (when the person holds the end still, this is called a closed reflection). Does it come back as a 'right' or 'left' pulse?
L
R
WAVE SIMULATION TIME!!!
Post­Lab Slinky.notebook
February 08, 2013
6. Have the person with the string end hold the slinky by pulling lightly on the string (about 1 ½ feet from the slinky). The OTHER holder should transmit a single transverse pulse. Describe what happens when the pulse reaches the far end (when the end attached to the string is allowed to move, this is called an open reflection). Does it come back as a 'right' or 'left' pulse?
WAVE SIMULATION TIME!!!
Post­Lab Slinky.notebook
February 08, 2013
7. Have one holder send a transverse pulse while the other holder sends a longitudinal pulse at the same time. What happens to the two waves?
They Pass Right Through Each Other!!!
Post­Lab Slinky.notebook
February 08, 2013
8. Both holders should now transmit a transverse pulse at the same time. 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? Back to the SIMULATION!!!
Post­Lab Slinky.notebook
February 08, 2013
Constructive Interference:
+
Post­Lab Slinky.notebook
February 08, 2013
Constructive Interference:
+
When Nodes and
Antinodes peferctly
allign (overlap), we
get this:
=
Post­Lab Slinky.notebook
February 08, 2013
9. Both holders should again transmit a transverse pulse at the same time. However, this time 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? Yep, we can simulate this too!!!
Post­Lab Slinky.notebook
February 08, 2013
Destructive Interference:
+
Post­Lab Slinky.notebook
February 08, 2013
Destructive Interference:
+
When Nodes and
Antinodes peferctly
allign (overlap), we
get this:
=
Post­Lab Slinky.notebook
February 08, 2013
Post­Lab Slinky.notebook
February 08, 2013
10. You need to use a shorter section of slinky for this part. Gather up about half of the long slinky and sit closer together. One of the holders should move the slinky left and right until a single "hump" moves back and forth between the holders. Some adjustment in timing will be necessary until the wave is formed. This is called a standing wave because the endpoints don’t move. It is called a fundamental because it is the most basic wave that can be formed on this slinky (you could also call it a first harmonic).
Fundamental/First Harmonic
Second Harmonic
Third Harmonic
Post­Lab Slinky.notebook
February 08, 2013
How are Standing Waves Created?
In our lab, you had to vibrate the slinky in just the right way. Standing waves occur when you generate waves that perfectly interfere, both constuctively and destructively.
In other words, YOU vibrate the slinky exactly how the slinky is already vibrating!!!
Click to see how standing waves are made
Post­Lab Slinky.notebook
February 08, 2013
How are Standing Waves Created?
If we generate
waves like this:
1.
They
reflect
back like
this:
2.
3.
They CONSTRUCTIVELY and
DESTRUCTIVELY interfere
like this:
Post­Lab Slinky.notebook
February 08, 2013
10. How many points on the wave move the maximum distance from the stationary slinky position (antinodes)? ______ How many points on the wave do not move at all from the stationary slinky position (nodes­this includes end­points)? ______
Fundamental/First Harmonic
Post­Lab Slinky.notebook
February 08, 2013
10. How many points on the wave move the maximum distance 1
from the stationary slinky position (antinodes)? ______ How many points on the wave do not move at all from the stationary slinky position (nodes­this includes end­points)? 2
______
Fundamental/First Harmonic
Post­Lab Slinky.notebook
February 08, 2013
10. This fundamental is only half of a complete wave. Consider the length of the slinky to be L. Describe the wavelength of the fundamental in terms of L. (wavelength=L x ??)
L
Fundamental/First Harmonic
Post­Lab Slinky.notebook
February 08, 2013
10. This fundamental is only half of a complete wave. Consider the length of the slinky to be L. Describe the wavelength of the fundamental in terms of L. (wavelength=L x ??)
L
L
Post­Lab Slinky.notebook
February 08, 2013
10. This fundamental is only half of a complete wave. Consider the length of the slinky to be L. Describe the wavelength of the fundamental in terms of L. (wavelength=L x ??)
L
L
λ= Lx2
or
λ = 2L
Post­Lab Slinky.notebook
February 08, 2013
11. If you increase the speed of the oscillations (frequency), you will increase the number of humps. Increase the frequency until you get a waveform with two "humps". Some adjustment in timing will be necessary until the wave is formed. This standing wave is called the second harmonic.
How many antinodes are there? ______
How many nodes are there? ______
Second Harmonic
Post­Lab Slinky.notebook
February 08, 2013
11. If you increase the speed of the oscillations (frequency), you will increase the number of humps. Increase the frequency until you get a waveform with two "humps". Some adjustment in timing will be necessary until the wave is formed. This standing wave is called the second harmonic.
2
How many antinodes are there? ______
3
How many nodes are there? ______
Second Harmonic
Post­Lab Slinky.notebook
February 08, 2013
11. Describe the wavelength of the second harmonic in terms of L.
Post­Lab Slinky.notebook
February 08, 2013
11. Describe the wavelength of the second harmonic in terms of L.
L
Post­Lab Slinky.notebook
February 08, 2013
11. Describe the wavelength of the second harmonic in terms of L.
L
λ= Lx1
or
λ= L
Post­Lab Slinky.notebook
February 08, 2013
12. Try and get a standing wave with three "humps". This standing wave is called the third harmonic.
How many antinodes are there? ______
How many nodes are there? ______
Third Harmonic
Post­Lab Slinky.notebook
February 08, 2013
12. Try and get a standing wave with three "humps". This standing wave is called the third harmonic.
3
How many antinodes are there? ______
4
How many nodes are there? ______
Third Harmonic
Post­Lab Slinky.notebook
February 08, 2013
12. Describe the wavelength of the third harmonic in terms of L.
Post­Lab Slinky.notebook
February 08, 2013
12. Describe the wavelength of the third harmonic in terms of L.
L
Post­Lab Slinky.notebook
February 08, 2013
12. Describe the wavelength of the third harmonic in terms of L.
L
Only 2 /3 of L is required to complete a
wavelength, so:
Post­Lab Slinky.notebook
February 08, 2013
12. Describe the wavelength of the third harmonic in terms of L.
L
Only 2 /3 of L is required to complete a
wavelength, so:
λ = 2 /3 L
Post­Lab Slinky.notebook
13. Given the pattern for the above three activities, a) describe the number of antinodes for the nth harmonic (antinodes=n x ??).
First Harmonic
Second Harmonic
Third Harmonic
February 08, 2013
Post­Lab Slinky.notebook
February 08, 2013
13. Given the pattern for the above three activities, a) describe the number of antinodes for the nth harmonic (antinodes=n x ??).
First Harmonic
antinodes = n x 1
or just:
Second Harmonic
Third Harmonic
antinodes = n
Post­Lab Slinky.notebook
February 08, 2013
13. Given the pattern for the above three activities, b) describe the number of nodes for the nth harmonic.
First Harmonic
Second Harmonic
Third Harmonic
Post­Lab Slinky.notebook
February 08, 2013
13. Given the pattern for the above three activities, b) describe the number of nodes for the nth harmonic.
First Harmonic
Second Harmonic
Third Harmonic
nodes = n + 1
Post­Lab Slinky.notebook
February 08, 2013
13. Given the pattern for the above three activities, c) describe the wavelength of the nth harmonic in terms of L.
λ = 2L
First Harmonic
λ= L
Second Harmonic
λ = 2 /3 L
Third Harmonic
Post­Lab Slinky.notebook
February 08, 2013
13. Given the pattern for the above three activities, c) describe the wavelength of the nth harmonic in terms of L.
HINT:
λ = 2L
= 2 /1 L
First Harmonic
λ= L
=2 /2 L
Second Harmonic
λ = 2 /3 L
Third Harmonic
=2 /3 L
Post­Lab Slinky.notebook
February 08, 2013
13. Given the pattern for the above three activities, c) describe the wavelength of the nth harmonic in terms of L.
HINT:
λ = 2L
= 2 /1 L
λ=2 /n L
First Harmonic
λ= L
OR:
=2 /2 L
Second Harmonic
L = nλ/2
λ = 2 /3 L
Third Harmonic
Solution:
=2 /3 L
Post­Lab Slinky.notebook
February 08, 2013
Changing the length of the object that vibrates
changes its wavelength. What does that mean
to us?
Post­Lab Slinky.notebook
February 08, 2013
Things that vibrate differently, SOUND
differently (if we can hear them)!!!
The length of
the bells
increases as we
move from
right to left.
What happens
to the λ?
Post­Lab Slinky.notebook
February 08, 2013
A VERY simplified Demo:
Length vs. Wavelength
Post­Lab Slinky.notebook
February 08, 2013
14. One of the holders should transmit a transverse pulse by rapidly moving the end of 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 the slinky and determine the velocity (remember the pulse made a round trip). Repeat, adding 0.5 meters each time, and fill in the data table below.
Post­Lab Slinky.notebook
February 08, 2013
Post­Lab Slinky.notebook
February 08, 2013
On graph paper (provided), graph the velocity versus the length and draw a best­fit line. velocity (m/s)
Based on the shape of the graph, is there a relationship between the length of slinky and the velocity of the wave? What is the relationship?
Velocity vs. Length
2
1.5
1
0.5
3.5
4.0
4.5
5.0
length (m)
5.5
6.0
Post­Lab Slinky.notebook
February 08, 2013
Bonus Points:
Make an equation for the relationship between velocity and length based on your graph.
HINT:
y = mx + b
BUT WE ARE NOT MAKING
AND X-Y GRAPH, SO:
v = mL + b
Post­Lab Slinky.notebook
February 08, 2013
On graph paper (provided), graph the velocity versus the length and draw a best­fit line. velocity (m/s)
Based on the shape of the graph, is there a relationship between the length of slinky and the velocity of the wave? What is the relationship?
Velocity vs. Length
2
1.5
v = mL + b
1
0.5
3.5
4.0
4.5
5.0
length (m)
5.5
6.0
Post­Lab Slinky.notebook
We know that increasing the tension
of the slinky increases the velocity of
the wave pulse. What does increasing
the tension of a sound-producing
string do to the sound?
February 08, 2013
Post­Lab Slinky.notebook
February 08, 2013
Fundamental/First Harmonic
Second Harmonic
Third Harmonic
Fourth Harmonic
Fifth Harmonic
Attachments
wave­on­a­string_en.jar