|
Physics 109 - Standing Waves: Part II
|
Before this week's experiment, you will be using the online
tutor to do an Invention Exercise called 'Planet Phaedra'. The online tutor can be accessed at http://tutor.phas.ubc.ca
A data spreadsheet to be used in the Invention Exercise can be found at PlanetPhaedra_studentspreadsheet. Click on the link and open with your favourite spreadsheet program.
As usual, you get marks for the invention based on any good
try at it, not for any particular "right answer".
In week 1 you discovered that the power law relating frequency
and wavelength of a standing wave is that frequency is proportional
to the inverse wavelength. There are several ways to plot this, and
your task is to fit a function to the data for three distinct ways to
plot the data.
- Frequency versus wavelength: This plot has the
advantage that you are displaying just what you measured. However, the
function that would best fit the data is not completely obvious. Since
you do now know that frequency varies as 1/wavelength, fit the
appropriate model: frequency = c/wavelength. Use a spreadsheet program
and vary the parameter c until you get a good fit. What value of c
gives the best fit?
- Frequency versus 1/wavelength: This is a plot to do
if you think you know the power law. Fit a straight line on this plot
and again determine the value of c that gives the best fit.
- Log(frequency) versus Log(wavelength): This is the plot to do if
you suspect a power law is the correct function; power laws appear as
straight lines on a log-log plot and the slope of the line reveals what
power law it is. Fit a straight line on this plot to show that this is
an inverse power law. How does the parameter for the intercept relate
to the value of c determined above?
Next, you can get started on gathering next week's data.
The goal of part 2 is to discover the relationship between
the wave velocity and the tension in the wire. Take a few minutes
to think about how you will do this efficiently. Things you shuld
consider are
- plotting and analyzing the data as you go will help you
to make good time-management decisions.
- since you already know that frequency and wavelength can
determine velocity, you do not need an individual data set and
plot for each tension
- what measurements minimize the uncertainty in the results?
Marking Rubric
Planet Phaedra: 2 marks
remember, marks for your graphs require (data, uncertainty in the data, labelled
axes with units, caption, and the line or curve that fits the data)
Plot of frequency versus wavelength with a fit: 3 marks
Plot of frequency versus 1/wavelength with a fit: 3 marks
Log-log plot with a fit: 3 marks
Conclusion: 2 marks for conclusion, including the fitting functions,
value and units for all parameters, and interpretation of the fitting
parameters.