Experiment 4: Standing Waves

Introduction:
We generated various normal modes and analyzed the various resonant conditions for standing waves on a string.

Equipment:

-Pasco variable frequency wave driver
-String
-Pasco student function generator
-Weight set (grams)
-Pendulim clamp
-Pulley
-Digital Multimeter
-Meter stick

Procedure:

We took some initial measurements (mass and length of the string) and we set up the system. We then took various measurements for different harmonics (such as number of nodes, antinodes, wavelength) and we achieved such harmonics by adjusting the frequency of the function generator. This was done for two instances, the second of which was equivalent to one-fourth the original tension.

Data/Calculations:

We went through ten harmonics in case one and six in case two by toggling with the frequency generator. We recorded the frequencies that produced such harmonics and length from one node to another to calculate the wavelength. We also counted the number of nodes and anti-nodes and recorded them on the table above.

Above are the graphs we created by plotting the frequency versus one over the wavelength, the graph's slope should equal the wave speed.

We calculated the experimental values for their respective velocities using the formula shown above.

Above are the wave speeds from the graph and the wave speeds we calculated respectively. The experimental and theoretical values both seem to vary by a factor of two.

We can see from the table above that the experimental value of frequencies is around n times the frequency of the fundamental. Where n is the number of the harmonic.

The table above is obtained from taking the ratios between the frequencies in the first case and the ones in the second case. They also seem to differ by a factor of two.
Summary:
This experiment was surprisingly very accurate when comparing the values obtained from formulas and the values obtained from our observations. There are many factors that make them differ, however, such as wind resistance and the fact that we where conducting this experiment in a three dimensional space (the string not only oscillated, but also sort of spun in circles).