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cycles per second, the relationship is
1 cycle
1 _
T =

f
Maximum
equation 5.1 displacement
or
Rest
1 _
f = position

T Amplitude
equation 5.2 Maximum
displacement

EXAMPLE 5.1 Paper pulled this way
A vibrating system has a period of 0.5 s. What is the frequency in Hz?
FIGURE 5.4 A graph of simple harmonic motion is described
by a sinusoidal curve.
SOLUTION
1 _
T = 0.5 s f = a steady rate, the pen will draw a curve, as shown in Figure 5.4.

T

f = ? The greater the amplitude of the vibrating mass, the greater
1 _ the height of this curve. The greater the frequency, the closer

=

0.5 s
together the peaks and valleys. Note the shape of this curve. Th is
1 _ 1 _ shape is characteristic of simple harmonic motion and is called
=

0.5 s
a sinusoidal, or sine, graph. It is so named because it is the same
1 _ shape as a graph of the sine function in trigonometry.
= 2

s
= 2 Hz
5.2 WAVES
Most people, when they hear the word waves, imagine water
Simple harmonic motion of a vibrating object (such as the waves coming to a shore in an ongoing motion or perhaps the
motion of a mass on a spring) can be represented by a graph. water ripples on a lake where a rock hits the still water surface

This graph illustrates how the displacement of the object is (Figure 5.5). The water in such a lake is a medium in which the

changing with time. From the graph you can usually read the waves travel, but the medium itself does not travel. Th e rock
amplitude, the period, and the frequency of the waves. If a pen created an isolated disturbance of the medium. Because of the

is fixed to a vibrating mass and a paper is moved beneath it at disturbance, the molecules of the medium were set in periodic

FIGURE 5.5 A water wave moves across the surface. How do you know for sure that it is energy, not water, that is moving across the surface?

118 CHAPTER 5 Wave Motions and Sound 5-4