Use a nail to puncture a small hole in the bottom of a paper cup as well as two holes on opposite sides near the rim. (Alternatively, you may melt holes in a plastic cup with a nail that has been heated in the flame of a laboratory burner.) Tie a string through the upper holes as shown in Figure A and cover the bottom hole with a piece of tape. Fill the cup with dark sand or dilute paint. Place a sheet of white paper under the cup.
| Uncover
the hole and swing the cup in a small arc. If the sand or paint
does not leak fast enough to make an easily observable straight
track on the sheet, increase the diameter of the hole until it does. The swinging cup is a pendulum, and if the arc (amplitude) is small it will undergo simple harmonic motion as discussed in the chapter on periodic motion. Tie the cup to a support, unroll about one meter of white paper and position one end of this sheet perpendicular to the direction of the cup's swing. The middle of the sheet should be positioned directly under the resting cup. Pull the cup back to the edge of the paper, remove the tape over the hole, and allow the cup to swing as your partner slowly pulls the paper at constant speed in a direction perpendicular to the cup's swing, as illustrated in Figure A. |
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The trace left by the paint or sand will be a sine wave.such as shown in Figure B. The amplitude of the sine wave represents the maximum displacement of the pendulum (cup) from its rest position. The distance from crest (high point) to crest or from trough (low point) to trough is called the wavelength (l). How can you obtain a wave pattern with the same wavelength but with different amplitude? How can you obtain a wave pattern with the same amplitude but with a shorter wavelength? Experiment with the length of the pendulum and the speed at which the paper is moved until you obtain such wave patterns.
Frequency is a measure of the number of waves per unit
time and in this activity is determined by how rapidly the
pendulum swings. If the pendulum makes one complete swing in
a second the frequency is 1 vibration/s, also known as one cycle
per second or one hertz (1 Hz).
The period is the time required to make one vibration. Since frequency is the number of crests or troughs passing a given point in unit time, and period is the time between the passage of two successive crests or troughs, the relationship between frequency f and period T is reciprocal: f = 1/T or T = 1/f. How can you obtain a wave with a longer period? How can you obtain a wave with a higher frequency? Experiment with the length of the pendulum and the speed at which the paper is moved until you obtain such wave patterns.