Exploratories

Wave Characteristics

Problems
:

Wavelength, amplitude, frequency, period, crest, trough.

Materials:

Small plastic or paper cup, string, sand or paint, rolls of white paper about 30 cm wide.

Principles and Procedures:

Part 1. Picturing transverse waves:

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.

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.

Part 2. Transverse waves in water.

Fill a rectangular pan with water to a depth of about 1.5 cm. Place the pan on a level surface. Cut a wooden dowel (2-cm diameter or thicker) to a length slightly less than the width of the pan and place the dowel in the water at one end. Touch a finger to the dowel and roll it back and forth once and observe the transverse wave move across the water's surface. Roll the dowel back and forth repeatedly and observe the train of waves moving across the water's surface.
The speed of a wave through a given medium is constant. Roll the dowel back and forth at a slow rate and note the length of the wave generated. Roll the dowel back and forth faster (increased frequency) and note that the wavelength is shorter. Roll the dowel even faster and note that the wavelength is shorter yet. These activities show that there is an important relationship between the speed of a wave and the frequency and wavelength (wave speed = frequency x wavelength). If v is speed, f is frequency, and
l is wavelength we have: v = fl. This fundamental relationship is true for waves of any type propagating through any medium, even for electromagnetic waves such as light, which require no material medium for propagation.

Summing Up:

1. What is a wave? A crest? A trough?

2. Describe the changes in the waves as you increased the amplitude of the pendulum's swing. Describe the change in the waves as your partner pulled the paper faster and faster when the pendulum/s length was the same.

3. Describe and distinguish between the following characteristics of a wave: frequency, period, amplitude, wavelength.

4. How are the frequency and period of a wave related? In what units are frequency and period measured?