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OVERVIEW

Sometimes you can feel the floor of a building shake for a moment when something heavy is dropped. You can also
feel prolonged vibrations in the ground when a nearby train moves by. The floor of a building and the ground are
solids that transmit vibrations from a disturbance. Vibrations are common in most solids because the solids are
elastic, having a tendency to rebound, or snap back, after a force or an impact deforms them. Usually you cannot see
the vibrations in a floor or the ground, but you sense they are there because you can feel them.
There are many examples of vibrations that you can see. You can see the rapid blur of a vibrating guitar string
(Figure 5.1). You can see the vibrating up-and-down movement of a bounced upon diving board. Both the vibrating
guitar string and the diving board set up a vibrating motion of air that you identify as a sound. You cannot see the
vibrating motion of the air, but you sense it is there because you hear sounds.
There are many kinds of vibrations that you cannot see but can sense. Heat, as you have learned, is associated
with molecular vibrations that are too rapid and too tiny for your senses to detect other than as an increase in
temperature. Other invisible vibrations include electrons that vibrate, generating spreading electromagnetic radio
waves or visible light. Thus, vibrations not only are observable motions of objects but also are characteristics of sound,
heat, electricity, and light. The vibrations involved in all these phenomena are alike in many ways, and all involve
energy. Therefore, many topics of physical science are concerned with vibrational motion. In this chapter, you will
learn about the nature of vibrations and how they produce waves in general. These concepts will be applied to sound
in this chapter and to electricity, light, and radio waves in later chapters.

5.1 FORCES AND ELASTIC MATERIALS are involved in vibrations, consider the spring and mass in Fig-

ure 5.2. The spring and mass are arranged so that the mass can
If you drop a rubber ball, it bounces because it is capable of recov- freely move back and forth on a frictionless surface. When the
ering its shape when it hits the floor. A ball of clay, on the other mass has not been disturbed, it is at rest at an equilibrium posi-

hand, does not recover its shape and remains a flattened blob on tion (Figure 5.2A). At the equilibrium position, the spring is not
the fl oor. An elastic material is one that is capable of recovering compressed or stretched, so it applies no force on the mass. If,
its shape after a force deforms it. A rubber ball is elastic and a ball however, the mass is pulled to the right (Figure 5.2B), the spring

of clay is not elastic. You know a metal spring is elastic because is stretched and applies a restoring force on the mass toward the
you can stretch it or compress it and it recovers its shape. left . The farther the mass is displaced, the greater the stretch of

There is a direct relationship between the extent of the spring and thus the greater the restoring force. Th e restoring

stretching or compression of a spring and the amount of force force is proportional to the displacement and is in the opposite
applied to it. A large force stretches a spring a lot; a small force direction of the applied force.
stretches it a little. As long as the applied force does not exceed If the mass is now released, the restoring force is the only
the elastic limit of the spring, the spring will always return to force acting (horizontally) on the mass, so it accelerates back
its original shape when you remove the applied force. Th ere toward the equilibrium position. This force will continuously

are three important considerations about the applied force and decrease until the moving mass arrives back at the equilibrium
the response of the spring: position, where the force is zero (Figure 5.2C). The mass will

have a maximum velocity when it arrives, however, so it over-

1. The greater the applied force, the greater the compression
shoots the equilibrium position and continues moving to the
or stretch of the spring from its original shape.
left (Figure 5.2D). As it moves to the left of the equilibrium posi-

2. The spring appears to have an internal restoring force, which
tion, it compresses the spring, which exerts an increasing force
returns it to its original shape.
on the mass. The moving mass comes to a temporary halt, but

3. The farther the spring is pushed or pulled, the stronger the
now the restoring force again starts it moving back toward the
restoring force that returns the spring to its original shape.
equilibrium position. The whole process repeats itself again and

again as the mass moves back and forth over the same path.
FORCES AND VIBRATIONS The vibrating mass and spring system will continue to

A vibration is a back-and-forth motion that repeats itself. vibrate for a while, slowly decreasing with time until the vibra-

A motion that repeats itself is called periodic motion. Such a tions stop completely. The slowing and stopping is due to air
motion is not restricted to any particular direction, and it can resistance and internal friction. If these could be eliminated

be in many different directions at the same time. Almost any or compensated for with additional energy, the mass would
solid can be made to vibrate if it is elastic. To see how forces continue to vibrate in periodic motion indefi nitely.
116 CHAPTER 5 Wave Motions and Sound 5-2