Unformatted text preview: nt waves, as shown in Figure 16.1.
If you count the number of seconds between the arrivals of two adjacent
waves, you are measuring the period T of the waves. In general, the period is the
time required for two identical points (such as the crests) of adjacent waves
to pass by a point.
The same information is more often given by the inverse of the period, which
is called the frequency f. In general, the frequency of a periodic wave is the number of crests (or troughs, or any other point on the wave) that pass a given
point in a unit time interval. The maximum displacement of a particle of the
medium is called the amplitude A of the wave. For our water wave, this represents
the highest distance of a water molecule above the undisturbed surface of the water as the wave passes by.
Waves travel with a speciﬁc speed, and this speed depends on the properties of
the medium being disturbed. For instance, sound waves travel through roomtemperature air with a speed of about 343 m/s (781 mi/h), whereas they travel
through most solids with a speed greater than 343 m/s. 16.2 DIRECTION OF PARTICLE DISPLACEMENT One way to demonstrate wave motion is to ﬂick one end of a long rope that is under tension and has its opposite end ﬁxed, as shown in Figure 16.2. In this manner, a single wave bump (called a wave pulse) is formed and travels along the rope
with a deﬁnite speed. This type of disturbance is called a traveling wave, and Figure 16.2 represents four consecutive “snapshots” of the creation and propagation
of the traveling wave. The rope is the medium through which the wave travels.
Such a single pulse, in contrast to a train of pulses, has no frequency, no period,
and no wavelength. However, the pulse does have deﬁnite amplitude and deﬁnite
speed. As we shall see later, the properties of this particular medium that determine the speed of the wave are the tension in the rope and its mass per unit
length. The shape of the wave pulse changes very little as it travels along the rope.2
As the wave pulse travels, each small segment of the rope, as it is disturbed,
moves in a direction perpendicular to the wave motion. Figure 16.3 illustrates this
2 Strictly speaking, the pulse changes shape and gradually spreads out during the motion. This effect is
called dispersion and is common to many mechanical waves, as well as to electromagnetic waves. We do
not consider dispersion in this chapter. 493 16.2 Direction of Particle Displacement P P P P Figure 16.2 A wave pulse traveling
down a stretched rope. The shape of
the pulse is approximately unchanged
as it travels along the rope. Figure 16.3 A pulse traveling on a
stretched rope is a transverse wave. The direction of motion of any element P of the
rope (blue arrows) is perpendicular to the
direction of wave motion (red arrows). point for one particular segment, labeled P. Note that no part of the rope ever
moves in the direction of the wave.
A traveling wave that causes the particles of the disturbed medium to move perpendicular to the wave motion is called a transverse wave. Transverse wave Compare this with another type of wave — one moving down a long, stretched
spring, as shown in Figure 16.4. The left end of the spring is pushed brieﬂy to the
right and then pulled brieﬂy to the left. This movement creates a sudden compression of a region of the coils. The compressed region travels along the spring (to
the right in Figure 16.4). The compressed region is followed by a region where the
coils are extended. Notice that the direction of the displacement of the coils is parallel to the direction of propagation of the compressed region.
A traveling wave that causes the particles of the medium to move parallel to the
direction of wave motion is called a longitudinal wave.
Sound waves, which we shall discuss in Chapter 17, are another example of
longitudinal waves. The disturbance in a sound wave is a series of high-pressure
and low-pressure regions that travel through air or any other material medium.
Compressed Compressed Stretched Stretched λ Figure 16.4 A longitudinal wave along a stretched spring. The displacement of the coils is in
the direction of the wave motion. Each compressed region is followed by a stretched region. Longitudinal wave 494 CHAPTER 16 Wave Motion Wave motion
Crest Trough Figure 16.5 The motion of water molecules on the surface of deep water in which a wave is
propagating is a combination of transverse and longitudinal displacements, with the result that
molecules at the surface move in nearly circular paths. Each molecule is displaced both horizontally and vertically from its equilibrium position. QuickLab
Make a “telephone” by poking a small
hole in the bottom of two paper cups,
threading a string through the holes,
and tying knots in the ends of the
string. If you speak into one cup
while pulling the string taut, a friend
can hear your voice in the other cup.
What kind of wave is present in the
string? Some waves in nature exhibit a combinat...
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- Spring '09
- Physics, pulse, wave function