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DESCRIBING VIBRATIONS
A motion of a vibrating mass is described by measuring three
basic quantities called the amplitude of vibration (amplitude
for short), the period, and the frequency of vibration (see Fig-
ure 5.3). The amplitude is the largest displacement from the

equilibrium position (rest position) that the mass can have
in this motion. All other displacements that you may see and
measure, when observing a vibrating mass, are smaller than
the amplitude.
A complete vibration is called a cycle. A cycle is the move-

ment from some point, say the far left, all the way to the far
right and back to the same point again, the far left in this

example. Th e period (T) is the number of seconds per cycle.
For example, suppose 0.1 s is required for an object to move
through one complete cycle, to complete the motion from one
point, then back to that point. The period of this vibration is

0.1 s. In other words, the period T is the time of one full cycle
or one full vibration.
Sometimes it is useful to know how frequently a vibration

completes a cycle every second. The number of cycles per sec-
ond is called the frequency ( f ). For example, a vibrating object

moves through 10 cycles in 1 s. The frequency of this vibration
FIGURE 5.1 Vibrations are common in many elastic materials, is 10 cycles per second. Frequency is measured in a unit called
and you can see and hear the results of many in your surroundings.

Other vibrations in your surroundings, such as those involved in a hertz (Hz). The unit for a hertz is 1/s since a cycle does not

heat, electricity, and light, are invisible to the senses. have dimensions. Thus, a frequency of 10 cycles per second is
referred to as 10 hertz or 10 1/s. In other words, frequency f tells
you how many full vibrations (or full cycles) are performed in
1 second.
The periodic vibration, or oscillation, of the mass is similar

to many vibrational motions found in nature called simple har- The period and frequency are two ways of describing the
monic motion. Simple harmonic motion is defined as the vibratory time involved in a vibration. Since the period (T) is the num-

motion that occurs when there is a restoring net force opposite ber of seconds per cycle and the frequency (f ) is the number of
to and proportional to a displacement.

Maximum Rest Maximum
displacement position displacement
A
Amplitude

B

Period: time
C for 1 cycle 1 cycle or
vibration

Frequency:
cycles/s
D
FIGURE 5.3 A vibrating mass attached to a spring is
FIGURE 5.2 A mass on a frictionless surface is at rest at displaced from the rest or equilibrium position and then released.
an equilibrium position (A) when undisturbed. When the spring The maximum displacement is called the amplitude of the
is stretched (B) or compressed (D), then released (C), the mass vibration. A cycle is one complete vibration. The period is the
vibrates back and forth because restoring forces pull opposite to number of seconds per cycle. The frequency is a count of how
and proportional to the displacement. many cycles are completed in 1 s.

5-3 CHAPTER 5 Wave Motions and Sound 117