Core Unit II: Wave Motion

A. Properties of Waves

1. Wave Terminology

Key Concepts

A wave is a transfer of energy, in the form of a disturbance, through some medium, without translocation of the medium.

A wave having a short duration is called a pulse.

Waves that vibrate in repeating cycles illustrate periodic motion or harmonic motion.

One complete oscillation is called a cycle.

Transverse vibration occurs when vibration of the medium is perpendicular to the direction of energy transfer. The maximum and minimum positions on a transverse wave are called the crest and trough.

Longitudinal vibration occurs when the medium vibrates parallel to the direction of energy transfer. Longitudinal vibrations consist of regions of compression and rarefaction.

Frequency (f) describes the number of cycles occurring in a given unit of time.

The SI unit for frequency is the hertz (Hz). The units s^-1 or cycles/second are also used.

Frequency =	Number of cycles
	Time Interval

The period (T) is the time required to complete one full cycle.

Period and frequency exhibit a reciprocal relationship.

The period of a simple pendulum is given by

where l is the length of the pendulum and g is the acceleration due to gravity. (This equation is true only if the amplitude is low.)

The amplitude of a wave is the maximum displacement from the equilibrium or rest position.

Two sources of wave motion are in phase if, at any moment, they have the same fractional displacement from the rest position and are moving in the same direction. If both conditions are not met the sources are out of phase.

The wavelength () is the distance between successive crests or successive troughs.

The wavelength is the shortest distance between two points in phase (or two points that have identical characteristics).

Learning Outcomes

Students will increase their abilities to:

1. Define the following terms: wave, disturbance, medium, pulse, vibration, cycle, periodic motion, simple harmonic motion, transverse vibration, longitudinal vibration, crest, trough, compression, rarefaction, frequency, period, amplitude, phase, wavelength.

2. Give examples of periodic motion.

3. Apply the correct units for period and frequency in problem solving and applications.

4. Solve problems involving period, frequency, and wave motion.

Teaching Suggestions, Activities and Demonstrations

1. Use a simple pendulum to illustrate the concepts of period and frequency.

2. Experimentally investigate the frequency and period of a simple pendulum, or some other object which undergoes harmonic motion.

3. Perform an activity to observe and record the characteristics of transverse, longitudinal, or torsional waves acting in one dimension.

   Various wave types can be illustrated using waves on a spring or a rope. Simple demonstrations and activities involving such apparatus can also be used to reinforce the use of proper wave terminology.

4. Design and conduct and experiment to measure the amplitude of a wave in one dimension.

5. Set up a demonstration which will allow students to determine if two wave sources, or two points on a wave pattern, are vibrating in phase.