# 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

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.