16 - Wave Motion

1 if you count the number of seconds between the

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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. λ 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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