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CHARACTERISTICS OF WAVE MOTION

The two types of wave motion, transverse and longitudinal, have many of the same characteristics, such as frequency, amplitude, and wavelength. Another important characteristic that these two types of wave motion share is VELOCITY. Velocity of propagation is the rate at which the disturbance travels through the medium, or the velocity with which the crest of the wave moves along. The velocity of the wave depends both on the type of wave (light, sound, or radio) and type of medium (air, water, or metal). If longitudinal waves are plotted as a graph, they appear as transverse waves. This fact is illustrated in figure 1-8.

Figure 1-8. - Longitudinal wave represented graphically by a transverse wave.

The frequency of a longitudinal wave, like that of a transverse wave, is the number of complete cycles the wave makes during a specific unit of time. The higher the frequency, the greater is the number of compressions and expansions per unit of time.

In the two types of wave motion described in the preceding discussion, the following quantities are of interest:

  • The PERIOD, which is the time (T) in which one complete vibratory cycle of events occurs,
  • The FREQUENCY OF VIBRATION (f), which is the number of cycles taking place in one second, and
  • The WAVELENGTH, which is the distance the disturbance travels during one period of vibration.

Now, consider the following concept. If a vibrating object makes a certain number of vibrations per second, then 1 second divided by the number of vibrations is equal to the period of time of 1 vibration. In other words, the period, or time, of 1 vibration is the reciprocal of the frequency; thus,

If you know the velocity of a wave, you can determine the wavelength by dividing the velocity by the frequency. As an equation:

When you use the above equation, be careful to express velocity and wavelength in the proper units of length.

For example, in the English system, if the velocity (expressed in feet per second) is divided by the frequency (expressed in cycles per second, or Hz), the wavelength is given in feet per cycle. If the metric system is used and the velocity (expressed in meters per second) is divided by the frequency (expressed in cycles per second), the wavelength is given in meters per cycle. Be sure to express both the wavelength and the frequency in the same units. (Feet per cycle and meters per cycle are normally abbreviated as feet or meters because one wavelength indicates one cycle.) Because this equation holds true for both transverse and longitudinal waves, it is used in the study of both electromagnetic waves and sound waves.

Consider the following example. Two cycles of a wave pass a fixed point every second, and the velocity of the wave train is 4 feet per second. What is the wavelength? The formula for determining wavelength is as follows:

Note: In problems of this kind, be sure NOT to confuse wave velocity with frequency. FREQUENCY is the number of cycles per unit of time (Hz). WAVE VELOCITY is the speed with which a wave train passes a fixed point.

Here is another problem. If a wave has a velocity of 1,100 feet per second and a wavelength of 30 feet, what is the frequency of the wave?

By transposing the general equation:

To find the velocity, rewrite the equation as: v = lf

Let's work one more problem, this time using the metric system.

Suppose the wavelength is 0.4 meters and the frequency is 12 kHz.

What is the velocity?

Use the formula:

Other important characteristics of wave motion are reflection, refraction, diffraction, and the Doppler effect. Big words, but the concept of each is easy to see. For ease of understanding, we will explain the first two characteristics using light waves, and the last two characteristics using sound waves. You should keep in mind that all waves react in a similar manner.

Within mediums, such as air, solids, or gases, a wave travels in a straight line. When the wave leaves the boundary of one medium and enters the boundary of a different medium, the wave changes direction. For our purposes in this module, a boundary is an imaginary line that separates one medium from another.

When a wave passes through one medium and encounters a medium having different characteristics, three things can occur to the wave: (1) Some of the energy can be reflected back into the initial medium; (2) some of the energy can be transmitted into the second medium where it may continue at a different velocity; or (3) some of the energy can be absorbed by the medium. In some cases, all three processes (reflection, transmission, and absorption) may occur to some degree.

Reflection

REFLECTION WAVES are simply waves that are neither transmitted nor absorbed, but are reflected from the surface of the medium they encounter. If a wave is directed against a reflecting surface, such as a mirror, it will reflect or "bounce" from the mirror. Refer to figure 1-9. A wave directed toward the surface of the mirror is called the INCIDENT wave. When the wave bounces off of the mirror, it becomes known as the REFLECTED wave. An imaginary line perpendicular to the mirror at the point at which the incident wave strikes the mirror's surface is called the NORMAL, or perpendicular. The angle between the incident wave and the normal is called the ANGLE OF INCIDENCE. The angle between the reflected wave and the normal is called the ANGLE OF REFLECTION.

Figure 1-9. - Reflection of a wave.

If the reflecting surface is smooth and polished, the angle between the incident ray and the normal will be the same as the angle between the reflected ray and the normal. This conforms to the law of reflection which states: The angle of incidence is equal to the angle of reflection.

The amount of incident wave energy reflected from a given surface depends on the nature of the surface and the angle at which the wave strikes the surface. As the angle of incidence increases, the amount of wave energy reflected increases. The reflected energy is the greatest when the wave is nearly parallel to the reflecting surface. When the incident wave is perpendicular to the surface, more of the energy is transmitted into the substance and less is reflected. At any incident angle, a mirror reflects almost all of the wave energy, while a dull, black surface reflects very little.

Q.11 What is the law of reflection? answer.gif (214 bytes)
Q.12 When a wave is reflected from a surface, energy is transferred. When is the transfer of energy greatest? answer.gif (214 bytes)
Q.13 When is the transfer of energy minimum? answer.gif (214 bytes)




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