Basic Physics Lab 3:
Introduction
A string that is fixed at the ends can vibrate in a number of different patterns, each with its own frequency, called a resonant frequency. The prediction is that the frequencies form a harmonic sequence with
.1
where n is a positive integer and the linear density is the mass per unit length. In this lab you will measure the tension, the mass per unit length and the different resonant frequencies and see if equation 1 predicts the “correct” frequencies given the measured wave speed and the measured length of the string.
Experiment
1. Measure the length of your length L of bungee cord (unstretched) and measure its mass M. Use these to compute the linear density = M/L. (You instructor may just give you a length of the cord 3m long to “weigh”.)
2. Tie one end to a ring stand that is clamped to the table. Run the other end through the driver and over the pulley at the other end of the table and tie a knot in it so you can attach the mass hanger.
3. Tie two wire ties on the cord 1m apart. Now add the hanger and 600-700g and measure the distance between the two ties. The ratio of the two lengths is the distance it stretched. Compute a new liner density based on this ratio.
4. Set the dial for the amplitude of the amplifier on 0, i.e. all the way counter clockwise. Set the amplitude control on the function generator to its lowest level, again all the way CCW. Turn on the function generator and set the frequency multiplier on 1Hz and press the -20dB button. (We do not want to drive the vibrator to too large an amplitude. You can damage it if you do.)
5. Now set the frequency to 5Hz and turn the amplitude dial on the amplifier about ¼ turn and the amplitude dial on the function generator about ¼ turn. You should be able to see the shaft on the vibrator go up and down. Gradually increase the frequency until you find the first normal mode and record its frequency. Record its shape.
6. Increase the frequency and find the second normal mode. Record its frequency and shape. Continue to do this for the first 6 or 7 modes. When you have finished, turn the amplitude dial on the amplifier to 0 (CCW).
Analysis
Make a table of the mode numbers, the measured frequencies for each mode and the expected frequencies based on equation 1 something like the table below. (How close are the expected frequencies to the measured frequencies?)
|
Mode Number |
Measured f (HZ) |
Expected f (Hz) |
Percent diff. |
|
|
|
|
|
Plot the measured frequencies vs. the mode number. This should be a straight line and the slope should be the first harmonic. Is it? (Compare it to the measured first harmonic and the expected first harmonic. Is it within 2 standard deviations of the expected first harmonic?)