Lab Experiment - Standing Waves on a String

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Recap
Lab Experiment - Standing Waves on a String
Lab Experiment
Standing Waves on a String
Terry Sturtevant
Wilfrid Laurier University
January 16, 2014
Terry Sturtevant
Lab Experiment Standing Waves on a String
Recap
Lab Experiment - Standing Waves on a String
What was important in the PC131 labs?
Terry Sturtevant
Lab Experiment Standing Waves on a String
Recap
Lab Experiment - Standing Waves on a String
What was important in the PC131 labs?
1
uncertainties in measurements
Terry Sturtevant
Lab Experiment Standing Waves on a String
Recap
Lab Experiment - Standing Waves on a String
What was important in the PC131 labs?
1
uncertainties in measurements
precision measure for digital instruments
Terry Sturtevant
Lab Experiment Standing Waves on a String
Recap
Lab Experiment - Standing Waves on a String
What was important in the PC131 labs?
1
uncertainties in measurements
precision measure for digital instruments
precision measure for analog instruments
Terry Sturtevant
Lab Experiment Standing Waves on a String
Recap
Lab Experiment - Standing Waves on a String
What was important in the PC131 labs?
1
uncertainties in measurements
precision measure for digital instruments
precision measure for analog instruments
2
uncertainty in the average
Terry Sturtevant
Lab Experiment Standing Waves on a String
Recap
Lab Experiment - Standing Waves on a String
What was important in the PC131 labs?
1
uncertainties in measurements
precision measure for digital instruments
precision measure for analog instruments
2
uncertainty in the average
bigger of the precision measure and the standard deviation of
the mean
Terry Sturtevant
Lab Experiment Standing Waves on a String
Recap
Lab Experiment - Standing Waves on a String
What was important in the PC131 labs?
1
uncertainties in measurements
precision measure for digital instruments
precision measure for analog instruments
2
uncertainty in the average
bigger of the precision measure and the standard deviation of
the mean
how to improve the experiment
Terry Sturtevant
Lab Experiment Standing Waves on a String
Recap
Lab Experiment - Standing Waves on a String
What was important in the PC131 labs?
1
uncertainties in measurements
precision measure for digital instruments
precision measure for analog instruments
2
uncertainty in the average
bigger of the precision measure and the standard deviation of
the mean
how to improve the experiment
3
calculations with uncertainties
Terry Sturtevant
Lab Experiment Standing Waves on a String
Recap
Lab Experiment - Standing Waves on a String
What was important in the PC131 labs?
1
uncertainties in measurements
precision measure for digital instruments
precision measure for analog instruments
2
uncertainty in the average
bigger of the precision measure and the standard deviation of
the mean
how to improve the experiment
3
calculations with uncertainties
4
agreement of quantities with uncertainties
Terry Sturtevant
Lab Experiment Standing Waves on a String
Recap
Lab Experiment - Standing Waves on a String
What was important in the PC131 labs?
1
uncertainties in measurements
precision measure for digital instruments
precision measure for analog instruments
2
uncertainty in the average
bigger of the precision measure and the standard deviation of
the mean
how to improve the experiment
3
calculations with uncertainties
4
agreement of quantities with uncertainties
5
writing a lab report
Terry Sturtevant
Lab Experiment Standing Waves on a String
Recap
Lab Experiment - Standing Waves on a String
Parts of an experiment
Research questions
Why this experiment?
Equipment
Method
Parts of an experiment
Terry Sturtevant
Lab Experiment Standing Waves on a String
Recap
Lab Experiment - Standing Waves on a String
Parts of an experiment
Research questions
Why this experiment?
Equipment
Method
Parts of an experiment
Data collection
Terry Sturtevant
Lab Experiment Standing Waves on a String
Recap
Lab Experiment - Standing Waves on a String
Parts of an experiment
Research questions
Why this experiment?
Equipment
Method
Parts of an experiment
Data collection
Data transformation
Terry Sturtevant
Lab Experiment Standing Waves on a String
Recap
Lab Experiment - Standing Waves on a String
Parts of an experiment
Research questions
Why this experiment?
Equipment
Method
Parts of an experiment
Data collection
Data transformation
Data combination
Terry Sturtevant
Lab Experiment Standing Waves on a String
Recap
Lab Experiment - Standing Waves on a String
Parts of an experiment
Research questions
Why this experiment?
Equipment
Method
Parts of an experiment
Data collection
Data transformation
Data combination
Data analysis and interpretation
Terry Sturtevant
Lab Experiment Standing Waves on a String
Recap
Lab Experiment - Standing Waves on a String
Parts of an experiment
Research questions
Why this experiment?
Equipment
Method
Parts of an experiment
Data collection
Data transformation
Data combination
Data analysis and interpretation
The steps are the same as in PC131; the third one becomes a little
more involved.
Terry Sturtevant
Lab Experiment Standing Waves on a String
Recap
Lab Experiment - Standing Waves on a String
Parts of an experiment
Research questions
Why this experiment?
Equipment
Method
Research questions
Terry Sturtevant
Lab Experiment Standing Waves on a String
Recap
Lab Experiment - Standing Waves on a String
Parts of an experiment
Research questions
Why this experiment?
Equipment
Method
Research questions
1
What is the mass density of the string?
Terry Sturtevant
Lab Experiment Standing Waves on a String
Recap
Lab Experiment - Standing Waves on a String
Parts of an experiment
Research questions
Why this experiment?
Equipment
Method
Research questions
1
What is the mass density of the string?
This has a quantitative answer.
Terry Sturtevant
Lab Experiment Standing Waves on a String
Recap
Lab Experiment - Standing Waves on a String
Parts of an experiment
Research questions
Why this experiment?
Equipment
Method
Research questions
1
What is the mass density of the string?
This has a quantitative answer.
We’ll want to compare this with our expectations.
Terry Sturtevant
Lab Experiment Standing Waves on a String
Recap
Lab Experiment - Standing Waves on a String
Parts of an experiment
Research questions
Why this experiment?
Equipment
Method
Research questions
1
What is the mass density of the string?
This has a quantitative answer.
We’ll want to compare this with our expectations.
2
Can we tell which of the samples it matches?
Terry Sturtevant
Lab Experiment Standing Waves on a String
Recap
Lab Experiment - Standing Waves on a String
Parts of an experiment
Research questions
Why this experiment?
Equipment
Method
Research questions
1
What is the mass density of the string?
This has a quantitative answer.
We’ll want to compare this with our expectations.
2
Can we tell which of the samples it matches?
This has a qualitative answer.
Terry Sturtevant
Lab Experiment Standing Waves on a String
Recap
Lab Experiment - Standing Waves on a String
Parts of an experiment
Research questions
Why this experiment?
Equipment
Method
Research questions
1
What is the mass density of the string?
This has a quantitative answer.
We’ll want to compare this with our expectations.
2
Can we tell which of the samples it matches?
This has a qualitative answer.
We’ll want to discuss how this fits with our expectations.
Terry Sturtevant
Lab Experiment Standing Waves on a String
Recap
Lab Experiment - Standing Waves on a String
Parts of an experiment
Research questions
Why this experiment?
Equipment
Method
Research questions
1
What is the mass density of the string?
This has a quantitative answer.
We’ll want to compare this with our expectations.
2
Can we tell which of the samples it matches?
This has a qualitative answer.
We’ll want to discuss how this fits with our expectations.
There may be others that will come up along the way.
Terry Sturtevant
Lab Experiment Standing Waves on a String
Recap
Lab Experiment - Standing Waves on a String
Parts of an experiment
Research questions
Why this experiment?
Equipment
Method
Why this experiment?
Terry Sturtevant
Lab Experiment Standing Waves on a String
Recap
Lab Experiment - Standing Waves on a String
Parts of an experiment
Research questions
Why this experiment?
Equipment
Method
Why this experiment?
1
Appropriate physics for this course
Terry Sturtevant
Lab Experiment Standing Waves on a String
Recap
Lab Experiment - Standing Waves on a String
Parts of an experiment
Research questions
Why this experiment?
Equipment
Method
Why this experiment?
1
Appropriate physics for this course
2
Illustrates various graphical analysis principles
Terry Sturtevant
Lab Experiment Standing Waves on a String
Recap
Lab Experiment - Standing Waves on a String
Parts of an experiment
Research questions
Why this experiment?
Equipment
Method
Why this experiment?
1
Appropriate physics for this course
2
Illustrates various graphical analysis principles
The process is similar to that in PC131, with graphical analysis
added.
Terry Sturtevant
Lab Experiment Standing Waves on a String
Recap
Lab Experiment - Standing Waves on a String
Parts of an experiment
Research questions
Why this experiment?
Equipment
Method
Equipment
Terry Sturtevant
Lab Experiment Standing Waves on a String
Recap
Lab Experiment - Standing Waves on a String
Parts of an experiment
Research questions
Why this experiment?
Equipment
Method
Equipment
Oscillating string
Terry Sturtevant
Lab Experiment Standing Waves on a String
Recap
Lab Experiment - Standing Waves on a String
Parts of an experiment
Research questions
Why this experiment?
Equipment
Method
Equipment
Oscillating string
Masses
Terry Sturtevant
Lab Experiment Standing Waves on a String
Recap
Lab Experiment - Standing Waves on a String
Parts of an experiment
Research questions
Why this experiment?
Equipment
Method
Equipment
Oscillating string
Masses
Samples of “known” strings
Terry Sturtevant
Lab Experiment Standing Waves on a String
Recap
Lab Experiment - Standing Waves on a String
Parts of an experiment
Research questions
Why this experiment?
Equipment
Method
Equipment
Oscillating string
Masses
Samples of “known” strings
There are a few other pieces as well.
Terry Sturtevant
Lab Experiment Standing Waves on a String
Recap
Lab Experiment - Standing Waves on a String
Parts of an experiment
Research questions
Why this experiment?
Equipment
Method
Oscillator
Terry Sturtevant
Lab Experiment Standing Waves on a String
Recap
Lab Experiment - Standing Waves on a String
Parts of an experiment
Research questions
Why this experiment?
Equipment
Method
string
Oscillator
Terry Sturtevant
Lab Experiment Standing Waves on a String
Recap
Lab Experiment - Standing Waves on a String
Parts of an experiment
Research questions
Why this experiment?
Equipment
Method
Oscillator (side view)
Terry Sturtevant
Lab Experiment Standing Waves on a String
Recap
Lab Experiment - Standing Waves on a String
Parts of an experiment
Research questions
Why this experiment?
Equipment
Method
string
Oscillator (side view)
Terry Sturtevant
Lab Experiment Standing Waves on a String
Recap
Lab Experiment - Standing Waves on a String
Parts of an experiment
Research questions
Why this experiment?
Equipment
Method
Cup and pulley
Terry Sturtevant
Lab Experiment Standing Waves on a String
Recap
Lab Experiment - Standing Waves on a String
pulley
Parts of an experiment
Research questions
Why this experiment?
Equipment
Method
-
Cup and pulley
Terry Sturtevant
Lab Experiment Standing Waves on a String
Recap
Lab Experiment - Standing Waves on a String
pulley
-
cup
-
Parts of an experiment
Research questions
Why this experiment?
Equipment
Method
Cup and pulley
Terry Sturtevant
Lab Experiment Standing Waves on a String
Recap
Lab Experiment - Standing Waves on a String
Parts of an experiment
Research questions
Why this experiment?
Equipment
Method
View from oscillator
Terry Sturtevant
Lab Experiment Standing Waves on a String
Recap
Lab Experiment - Standing Waves on a String
oscillator
Parts of an experiment
Research questions
Why this experiment?
Equipment
Method
-
View from oscillator
Terry Sturtevant
Lab Experiment Standing Waves on a String
Recap
Lab Experiment - Standing Waves on a String
pulley
-
oscillator
-
Parts of an experiment
Research questions
Why this experiment?
Equipment
Method
View from oscillator
Terry Sturtevant
Lab Experiment Standing Waves on a String
Recap
Lab Experiment - Standing Waves on a String
Parts of an experiment
Research questions
Why this experiment?
Equipment
Method
View from pulley
Terry Sturtevant
Lab Experiment Standing Waves on a String
Recap
Lab Experiment - Standing Waves on a String
oscillator
Parts of an experiment
Research questions
Why this experiment?
Equipment
Method
-
View from pulley
Terry Sturtevant
Lab Experiment Standing Waves on a String
Recap
Lab Experiment - Standing Waves on a String
oscillator
-
pulley
-
Parts of an experiment
Research questions
Why this experiment?
Equipment
Method
View from pulley
Terry Sturtevant
Lab Experiment Standing Waves on a String
Recap
Lab Experiment - Standing Waves on a String
Parts of an experiment
Research questions
Why this experiment?
Equipment
Method
String
Terry Sturtevant
Lab Experiment Standing Waves on a String
Recap
Lab Experiment - Standing Waves on a String
Parts of an experiment
Research questions
Why this experiment?
Equipment
Method
6
node
String
Terry Sturtevant
Lab Experiment Standing Waves on a String
Recap
Lab Experiment - Standing Waves on a String
6
node
Parts of an experiment
Research questions
Why this experiment?
Equipment
Method
6
antinode
String
Terry Sturtevant
Lab Experiment Standing Waves on a String
Recap
Lab Experiment - Standing Waves on a String
Parts of an experiment
Research questions
Why this experiment?
Equipment
Method
String near oscillator
Terry Sturtevant
Lab Experiment Standing Waves on a String
Recap
Lab Experiment - Standing Waves on a String
Parts of an experiment
Research questions
Why this experiment?
Equipment
Method
node?
String near oscillator
Terry Sturtevant
Lab Experiment Standing Waves on a String
Recap
Lab Experiment - Standing Waves on a String
Parts of an experiment
Research questions
Why this experiment?
Equipment
Method
node?
antinode?
String near oscillator
Terry Sturtevant
Lab Experiment Standing Waves on a String
Recap
Lab Experiment - Standing Waves on a String
Parts of an experiment
Research questions
Why this experiment?
Equipment
Method
node?
antinode?
other?
String near oscillator
Terry Sturtevant
Lab Experiment Standing Waves on a String
Recap
Lab Experiment - Standing Waves on a String
Parts of an experiment
Research questions
Why this experiment?
Equipment
Method
Method
Terry Sturtevant
Lab Experiment Standing Waves on a String
Recap
Lab Experiment - Standing Waves on a String
Parts of an experiment
Research questions
Why this experiment?
Equipment
Method
Method
Adjust mass and try to get a standing wave pattern.
Terry Sturtevant
Lab Experiment Standing Waves on a String
Recap
Lab Experiment - Standing Waves on a String
Parts of an experiment
Research questions
Why this experiment?
Equipment
Method
Method
Adjust mass and try to get a standing wave pattern.
Determine the wavelength and tension and their uncertainties.
Terry Sturtevant
Lab Experiment Standing Waves on a String
Recap
Lab Experiment - Standing Waves on a String
Parts of an experiment
Research questions
Why this experiment?
Equipment
Method
Method
Adjust mass and try to get a standing wave pattern.
Determine the wavelength and tension and their uncertainties.
Repeat until you get data for several different patterns.
Terry Sturtevant
Lab Experiment Standing Waves on a String
Recap
Lab Experiment - Standing Waves on a String
Parts of an experiment
Research questions
Why this experiment?
Equipment
Method
Method
Adjust mass and try to get a standing wave pattern.
Determine the wavelength and tension and their uncertainties.
Repeat until you get data for several different patterns.
Verify that your data are changing monotonically.
Terry Sturtevant
Lab Experiment Standing Waves on a String
Recap
Lab Experiment - Standing Waves on a String
Parts of an experiment
Research questions
Why this experiment?
Equipment
Method
Method
Adjust mass and try to get a standing wave pattern.
Determine the wavelength and tension and their uncertainties.
Repeat until you get data for several different patterns.
Verify that your data are changing monotonically.
Determine the mass densities of string samples.
Terry Sturtevant
Lab Experiment Standing Waves on a String
Recap
Lab Experiment - Standing Waves on a String
Parts of an experiment
Research questions
Why this experiment?
Equipment
Method
Method
Adjust mass and try to get a standing wave pattern.
Determine the wavelength and tension and their uncertainties.
Repeat until you get data for several different patterns.
Verify that your data are changing monotonically.
Determine the mass densities of string samples.
Verify that your string density is the same order of magnitude
as the samples.
Terry Sturtevant
Lab Experiment Standing Waves on a String
Recap
Lab Experiment - Standing Waves on a String
Parts of an experiment
Research questions
Why this experiment?
Equipment
Method
Method
Adjust mass and try to get a standing wave pattern.
Determine the wavelength and tension and their uncertainties.
Repeat until you get data for several different patterns.
Verify that your data are changing monotonically.
Determine the mass densities of string samples.
Verify that your string density is the same order of magnitude
as the samples.
Perform detailed analysis to get the density of your string to
compare with the samples.
Terry Sturtevant
Lab Experiment Standing Waves on a String
Recap
Lab Experiment - Standing Waves on a String
Parts of an experiment
Research questions
Why this experiment?
Equipment
Method
Method
Adjust mass and try to get a standing wave pattern.
Determine the wavelength and tension and their uncertainties.
Repeat until you get data for several different patterns.
Verify that your data are changing monotonically.
Determine the mass densities of string samples.
Verify that your string density is the same order of magnitude
as the samples.
Perform detailed analysis to get the density of your string to
compare with the samples.
Order of magnitude calculations in the lab ensure that your data
aren’t gibberish.
Terry Sturtevant
Lab Experiment Standing Waves on a String
Recap
Lab Experiment - Standing Waves on a String
Parts of an experiment
Research questions
Why this experiment?
Equipment
Method
What are the graphical analysis techniques?
Terry Sturtevant
Lab Experiment Standing Waves on a String
Recap
Lab Experiment - Standing Waves on a String
Parts of an experiment
Research questions
Why this experiment?
Equipment
Method
What are the graphical analysis techniques?
Linearizing the equation
Terry Sturtevant
Lab Experiment Standing Waves on a String
Recap
Lab Experiment - Standing Waves on a String
Parts of an experiment
Research questions
Why this experiment?
Equipment
Method
What are the graphical analysis techniques?
Linearizing the equation
Plotting a linear graph to see how well the data fit
Terry Sturtevant
Lab Experiment Standing Waves on a String
Recap
Lab Experiment - Standing Waves on a String
Parts of an experiment
Research questions
Why this experiment?
Equipment
Method
What are the graphical analysis techniques?
Linearizing the equation
Plotting a linear graph to see how well the data fit
Determining the slope and y -intercept from the graph using
least squares fitting
Terry Sturtevant
Lab Experiment Standing Waves on a String
Recap
Lab Experiment - Standing Waves on a String
Parts of an experiment
Research questions
Why this experiment?
Equipment
Method
What are the graphical analysis techniques?
Linearizing the equation
Plotting a linear graph to see how well the data fit
Determining the slope and y -intercept from the graph using
least squares fitting
Determining the uncertainties in the slope and y -intercept
from the graph using whichever technique is appropriate
Terry Sturtevant
Lab Experiment Standing Waves on a String
Recap
Lab Experiment - Standing Waves on a String
Parts of an experiment
Research questions
Why this experiment?
Equipment
Method
What are the graphical analysis techniques?
Linearizing the equation
Plotting a linear graph to see how well the data fit
Determining the slope and y -intercept from the graph using
least squares fitting
Determining the uncertainties in the slope and y -intercept
from the graph using whichever technique is appropriate
Calculating the mass density of your string (and its
uncertainty) using the linearization equations and your
graphical results
Terry Sturtevant
Lab Experiment Standing Waves on a String
Recap
Lab Experiment - Standing Waves on a String
Parts of an experiment
Research questions
Why this experiment?
Equipment
Method
What are the graphical analysis techniques?
Linearizing the equation
Plotting a linear graph to see how well the data fit
Determining the slope and y -intercept from the graph using
least squares fitting
Determining the uncertainties in the slope and y -intercept
from the graph using whichever technique is appropriate
Calculating the mass density of your string (and its
uncertainty) using the linearization equations and your
graphical results
After this it’s just a matter of comparing values and interpreting
the results.
Terry Sturtevant
Lab Experiment Standing Waves on a String
Recap
Lab Experiment - Standing Waves on a String
Parts of an experiment
Research questions
Why this experiment?
Equipment
Method
How do you determine the “best” linearization?
Terry Sturtevant
Lab Experiment Standing Waves on a String
Recap
Lab Experiment - Standing Waves on a String
Parts of an experiment
Research questions
Why this experiment?
Equipment
Method
How do you determine the “best” linearization?
How well the data points fit
Terry Sturtevant
Lab Experiment Standing Waves on a String
Recap
Lab Experiment - Standing Waves on a String
Parts of an experiment
Research questions
Why this experiment?
Equipment
Method
How do you determine the “best” linearization?
How well the data points fit
Which ones makes the uncertainties in the calculated results
smallest
Terry Sturtevant
Lab Experiment Standing Waves on a String
Recap
Lab Experiment - Standing Waves on a String
Parts of an experiment
Research questions
Why this experiment?
Equipment
Method
How do you determine the “best” linearization?
How well the data points fit
Which ones makes the uncertainties in the calculated results
smallest
These may not both indicate the same linearization as “best”.
Terry Sturtevant
Lab Experiment Standing Waves on a String
Recap
Lab Experiment - Standing Waves on a String
Parts of an experiment
Research questions
Why this experiment?
Equipment
Method
When is the lab report due?
Terry Sturtevant
Lab Experiment Standing Waves on a String
Recap
Lab Experiment - Standing Waves on a String
Parts of an experiment
Research questions
Why this experiment?
Equipment
Method
When is the lab report due?
Six weeks from now
Terry Sturtevant
Lab Experiment Standing Waves on a String
Recap
Lab Experiment - Standing Waves on a String
Parts of an experiment
Research questions
Why this experiment?
Equipment
Method
When is the lab report due?
Six weeks from now
You have two other exercises to do first
Terry Sturtevant
Lab Experiment Standing Waves on a String
Recap
Lab Experiment - Standing Waves on a String
Parts of an experiment
Research questions
Why this experiment?
Equipment
Method
When is the lab report due?
Six weeks from now
You have two other exercises to do first
What about the post-lab questions?
Terry Sturtevant
Lab Experiment Standing Waves on a String
Recap
Lab Experiment - Standing Waves on a String
Parts of an experiment
Research questions
Why this experiment?
Equipment
Method
When is the lab report due?
Six weeks from now
You have two other exercises to do first
What about the post-lab questions?
Not now; they will be part of the lab report.
Terry Sturtevant
Lab Experiment Standing Waves on a String
Recap
Lab Experiment - Standing Waves on a String
Parts of an experiment
Research questions
Why this experiment?
Equipment
Method
When is the lab report due?
Six weeks from now
You have two other exercises to do first
What about the post-lab questions?
Not now; they will be part of the lab report.
Terry Sturtevant
Lab Experiment Standing Waves on a String
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