Experiment 4: Standing Waves

The purpose of this lab was to investigate resonant standing waves that are driven by a frequency generator.

We used:
- Mechanical Vibrator
- Frequency Generator
- 50 gram hangar and weight set
- String
- 2 table clamps
- Rod
- Pulley
- Meter Stick

Below are a pictures of out experiment:

We first measured the mass and length of the string used in the experiment to find the linear density of the string.

We then assembled the string between the two supports with 200g total mass hanging on the end of the string. When we set the string to oscillate, we adjusted the frequency generator until the string oscillated in its fundamental node. We then recorded the oscillation frequency, number of nodes, the total length of the string participating in the oscillation for the first, second, third, etc. harmonics.  We then reduced the tension on the string to one fourth of its original tension for the second case and repeated the experiment.

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CASE #1:

The above table shows the nodes, frequency, and wavelength of the first case and below is the plot of the frequency versus 1/lambda. 

The slope of the line, 80.233, is the wave speed. Below I calculated the wave speed using the equation for the wave speed. 

The percent error for the wave speed is 29.0%.

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CASE #2:

The above table shows the nodes, frequency, and wavelength of the first case and below is the plot of the frequency versus 1/lambda. 

The slope of the line, 40.103, is the wave speed. Below I calculated the wave speed using the equation for the wave speed. 

The percent error for the wave speed at 1/4 the tension is 28.9%.

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We then calculated the ratios for the wave speeds for case 1 compared to case 2 which is equal to the expected wave speed ratio:

From the above tables for case 1 and case 2, we can see that the measured frequencies are equal to n*f_n, for the harmonics. The ratio of the frequency for the first, second, third, etc. harmonics for case 1 compared to case 2 was 2 as expected. 

The experimental values that we got were not exact, but they were precise because we still got the expected value for the wave ratios and we also had about the same value for our experimental error. The source of error in this lab was the fact that the hanging mass had some movement when the string was oscillating. This meant that at the end where the hanging mass was hanging, there was not an exact antinode for the wave.