Goals: 1) To determine the relationship between the frequency of standing waves on a helical spring and the number of antinodes in the standing wave pattern, and

2) to determine the wavelength and speed of the waves

Pre-lab: Format your lab report in advance. Include the following:

a. title

b. goals

c. method (List 5 things you expect to do to achieve the greatest accuracy in measuring frequency.)

d. table for data (Columns must be labeled clearly, including units in column headings. A sample table is shown below.)

e. analysis questions

Method: The method will be discussed in class. Briefly, you will generate standing wave patterns of 1, 2, and 3 antinodes on a spring fixed at one end. For each wave pattern, measure the frequency enough times to be confident of your result. Then find the average. Measure the frequency by timing a set number of oscillations and dividing the total time into that number. Develop a method of timing and oscillating that gives accurate results.

  Number of     Trial  Total Time   Ave. Frequency   
  Antinodes            (s)          (Hz)             
                 1                                   
      1        2                                     
               3                                     
      2        1                                     
               etc.                                  

Maintain the spring at constant stretch and length throughout the experiment. Measure the length as the horizontal distance from the fixed hand to the oscillator's

hand. You will use this later in

wavelength calculations.

Data: Include number of oscillations used and length of spring.

Analysis:

1) Use your calculator or a graphical analysis program to obtain a graph of

frequency vs. number of antinodes. (Which variable goes on the horizontal axis?)

Do a linear least-squares fit to the data. Make a LARGE sketch of the graph and

label the axes properly.

2) Write the equation relating frequency f and number of antinodes n. (NO x's or y's)

Use the slope and f-intercept of the fit, with correct units and significant figures.

3) Use the equation to calculate the frequency for a standing wave with 4 antinodes;

then measure it experimentally. % difference?

4) Make large sketches of the three standing wave patterns that you produced.

Keep the spring length constant, just as you did in your experiment. Knowing

the length of the spring, determine the wavelength of each pattern.

5) Calculate the speed of the wave for each standing wave pattern by using the

average frequency and the wavelength of the pattern.

6) Calculate the speed of the wave for a standing wave pattern of 4 antinodes.

Justify your prediction.

7) If you kept the distance from oscillator's hand to fixed hand the same but put

more tension on the spring by stretching it more,...

a) how would the wavelength of the standing wave patterns change? Why?

b) how would the speed of the waves change? Why?

c) how would the frequency of the standing wave pattern change? Why?