# Physics 109 - Standing Waves: Part I

### Part I

The simple apparatus on your lab bench will be used over the next three weeks to study standing waves. The wire is fixed at one end and has a movable fulcrum at the other end that allows you to change the length of the wire. Tension is provided by a mass hanging over a pulley at the adjustable end. There is a magnet at the fixed end and a function generator that passes alternating current through the wire. The AC current in the presence of the magnet produces an alternating force on the wire, which is your means of driving the wire back and forth.. When the function generator is operating at a frequency that matches one of the resonant frequencies of the wire, a standing wave will appear.
Your first measurement should proceed as follows:

• Place 400 g weight on the holder that sets the tension in the wire.
• Use the fulcrum to set the length of the vibrating section of wire to 70 cm
• Set the generator ampltude to its highest setting
• Vary the frequency of the function generator in order to search for the lowest frequency standing wave resonance of the wire.
• Record your estimate of the resonant frequency and its uncertainty (and explain how you chose these).
• Try several different amplitudes on the function generator and comment on its effect.
• Try removing the weight and placing it back on again - is the frequency repeatable
• After trying different amplitudes and moving the weights on and off, give your best estimate of the resonant frequency and its uncertainty and justify this.

The whole class should compare the measured resonant frequency. Do you all agree with one another? If not, figure out why and correct the issue.

### Part II

The physical system being studied here is a wire held fixed at its two ends. Transverse waves traveling along the wire are reflected from each end and as the waves bounce back and forth from end to end they usually interfere with each other destructively. At certain frequencies each reflected wave interferes constructively with the incoming wave and these build up into a standing wave. This is an example of a resonance phenomenon. For a fixed length of wire, the resonances are evenly spaced in frequency (denoted F1, F2, F3...) so the relationship between them is

Fn = n * F1

wher F1 is the lowest resonant frequency.

Find at least three resonant frequencies for the wire length of 70 cm and a mass of 400 grams. Are the frequencies in agreement with the equation above?

### Part III

Try a few other wire lengths to build up a set of data on resonant frequency versus wavelength, noting that

wavelength = (2/n) * (length of wire)

You need only a few different harmonics at each length to build a complete data set. Most importantly, try to span as wide a range of resonant frequency as possible.
Develop a linerized plot to show the relationship between frequency and wavelength (plotted as frequency versus something). Once you have a linearized plot, comment on the value and the meaning of the slope.

Marking Rubric

Critical assessment of how to do the measurment and how to determine uncertainty in the measurements: 3 mark
Measuring and comparing in part II 2 mark
Wide-ranging data set and graph 4 mark
Graphical rescaling to demonstrate frequency-wavelength relationship: 2 marks
Quantitative conclusion about frequency-wavelength relationship and comment on meaning of the slope: 2 marks