Main Equipment:
Tektronix Two Channel Digital Oscilloscope Model TDS210
Pasco Scientific Digital Function Generator PI9587C
Pasco Scientific Mechanical Vibrator Model SF-9324
Pasco Scientific Detector Model WA9613
Pasco Scientific Driver Model WA9613
Setup: In determining the dispersion of this system, we went through three different setups. In the first setup we used the Pasco mechanical vibrator model # SF-9324 to vibrate the wire. We clamped this vibrator down to a table in the optics lab to make sure that all of the vibrations from the mechanical vibrator were going into the rod. To drive the vibrator we used a digital function generator-amplifier model PI-9587. We attached the rod (Dr. Christian’s coat hanger) to the vibrator via a banana plug. We placed a meter stick directly behind this rod, at the same height and directly parallel in order to better measure the wavelength of the vibrations. To measure the amplitude of the oscillations, we placed a Pasco scientific detector model WA 9613 next to the wire. We attached this detector to a digital oscilloscope model TDS 210.
After collecting a few data points we decided to change the set up. We first decided to change the position of the detector. Placing it directly above the wire seemed to better facilitate reading the amplitude of the vibrating wire in the vertical direction. In fact, before, we had merely read the amplitude of the wire vibrating in the lateral direction, and not the vertical direction, as planned. We also decided to drive the wire with the Pasco magnetic driver model WA9613, in hopes of vibrating the rod to higher frequencies. To do this, we first clamped the banana plug end of the wire to a vise, and then clamped the Pasco driver to the same vise so that it sat directly below the wire. The magnetic driver, however, did not prove a more effective vibrator at high frequencies; it could not vibrate the rod at strong enough amplitudes to make the antinodes detectable. After taking several data points, then, we reverted back to vibrating the rod with the mechanical vibrator, maintaining the detector in the same position.
Below is a picture of the setup using the Pasco magnetic driver.
This is a close-up of the position of the Pasco scientific magnet detector relative to the rod.
Procedure: Before we started the experiment, we measured the length of the rod by measuring the relative positions of the fixed end and the free end of the rod with respect to the measuring stick behind it. To collect data, we varied the frequency to find where the rod exhibited resonance, measured the wavelength of the rod, recorded the frequency, and found the error in our frequency and wavelength measurements. Finding where the rod exhibited resonance, at the beginning, was fairly simple. We changed the frequency and saw with the eye when the anti-nodes on the rod were vibrating with the greatest amplitude. To aid our eyes, we used the Pasco magnet detector and measured exactly when the amplitude of the resonance was the greatest.
Below is a picture of a two-node standing wave (from http://www.phy.davidson.edu/StuHome/timv/IntLab/ChlaRes/main.htm)
comparable to the standing waves we saw in our experiment.
You can see the two nodes and the amplitude of the anti-node. The length from the fixed end node to the second node is the length of the anti-node. We then used this length to calculate the wavelength (wavelength = double the length of the anti-node).
As we tuned into higher frequencies, we could no longer see the nodes or antinodes of resonance. We came up with a quick solution by using little pieces of paper to locate the nodes. The papers would rattle up and down until they reached a node, where they remained still. We occasionally used a strobe light to aid in viewing the anti-nodes, and we also felt the rod to locate where it was vibrating (at anti-nodes), or not vibrating (at nodes). After determining the location of an anti-node, we placed the detector above that position, varied the frequency and found when there was a relative peak in the amplitude of vibration of the mode. To determine our error in frequency measurement, we found the range of frequency for which the amplitude of the vibration remained constant. To determine the error in measuring the wavelength, we measured the length of the node. To measure the wavelength of the rod, we placed the meter stick directly behind it to determine the relative positions of the anti-nodes. The wavelength, then, was determined as either double the length from anti-node to anti-node, or the length of two anti-nodes. At 39.2 Hz we decided to map out the dependence of the amplitude of the wire on frequency. We did this by using the delta function on the oscilloscope to measure the amplitude every 0.5 Hz.
Setup: We hung the mechanical vibrator upside down from a horizontal rod, so that the base of the vibrator was perpendicular to the table top. This rod was supported by two other rods with bases placed on the table, as shown below.
We used the same instruments from the previous experimental setup to drive the mechanical vibrator, detect the amplitude, and display it. The hoop of wire was attached to a banana plug, which connected to the mechanical vibrator. To get the detector as close as we could to the hoop without touching at resonant frequencies, we placed it face up on a series of blocks. To inhibit the occasional large movement of the hoop in the lateral direction, we placed two rods behind the hoop and one in front.
Procedure: First, we measured the circumference of the hoop with a piece of wire. The length of the wire is then the length over which standing waves were generated. Vibrating the hoop with the mechanical vibrator, we began to find its resonant frequencies. It was found that the hoop only resonated at odd mode numbers. This is the result of the apparatus; the banana plug connected to the vibrator locked the ends of the hoop in place, thereby making it a node at the source of excitation.
The wavelength of the standing waves generated was calculated knowing the relationship between the number of nodes and the length (circumference) of the hoop. We found the resonant frequency, measured the error in the frequency measurement, and measured the error in the wavelength as described in Part 1. Determining the resonant frequency, however, was a little more difficult; the frequency at which it the hoop vibrated seemed to depend on how quickly the frequency was changed on the function generator, as well previous vibrations. It should be noted, also, that the end of the hoop/wire broke twice while secured at the banana plug due to the stress on the wire caused by vibrations. To repair the hoop, we removed the broken part of the wire, reclamped the wire in loop form, remeasured the circumference of the hoop, and continued with the experiment.
Setup: We again placed the mechanical vibrator on a rod, parallel to the table, supported by two rods on either side. We positioned the mechanical vibrator with its base perpendicular to the table:
Using a banana clip and an alligator clip, we attached the beaded chain to the vibrator. We colored the beads on the chain in a red, green, blue, and black series so as to aid in measuring the wavelength at resonant frequencies. The function generator was again used to drive the vibrator.