Transverse and Longitudinal Waves

Transverse and Longitudinal Waves

A wave sent along a stretched, taut string is the simplest mechanical wave. If you give one end of a stretched string a single up-and-down jerk, a wave in the form of a single pulsetravels along the string. This pulse and its motion can occur because the string is under tension. When you pull your end of the string upward, it begins to pull upward on the adjacent section of the string via tension between the two sections. As the adjacent section moves upward, it begins to pull the next section upward, and so on. Meanwhile, you have pulled down on your end of the string. As each section moves upward in turn, it begins to be pulled back down-ward by neighboring sections that are already on the way down. The net result is that a distortion in the string’s shape (a pulse, as in Fig. 16-1a) moves along the string at some velocity . If you move your hand up and down in continuous simple harmonic motion, a continuous wave travels along the string at velocity . Because the motion of your hand is a sinusoidal function of time, the wave has a sinusoidal shape at any given instant, as in Fig. 16-1b; that is, the wave has the shape of a sine curve or a cosine curve.

We consider here only an “ideal” string, in which no friction-like forces within the string cause the wave to die out as it travels along the string. In addition, we as-sume that the string is so long that we need not consider a wave rebounding from the far end. One way to study the waves of Fig. 16-1 is to monitor the wave forms(shapes of the waves) as they move to the right. Alternatively, we could monitor the motion of an element of the string as the element oscillates up and down while a wave passes through it. We would find that the displacement of every such oscillat-ing string element is perpendicularto the direction of travel of the wave, as indicated in Fig. 16-1b. This motion is said to be transverse,and the wave is said to be a transverse wave.

Figure 16-2 shows how a sound wave can be produced by a piston in a long, air-filled pipe. If you suddenly move the piston rightward and then leftward, you can send a pulse of sound along the pipe. The rightward motion of the piston moves the elements of air next to it rightward, changing the air pressure there.The increased air pressure then pushes rightward on the elements of air some-what farther along the pipe. Moving the piston leftward reduces the air pressure next to it. As a result, first the elements nearest the piston and then farther elements move leftward. Thus, the motion of the air and the change in air pres-sure travel rightward along the pipe as a pulse. If you push and pull on the piston in simple harmonic motion, as is being done in Fig. 16-2, a sinusoidal wave travels along the pipe. Because the motion of the elements of air is parallel to the direction of the wave’s travel, the motion is said to be longitudinal, and the wave is said to be a longitudinal wave.In this chapter we focus on transverse waves, and string waves in particular; in Chapter 17 we focus on longitudinal waves, and sound waves in particular. Both a transverse wave and a longitudinal wave are said to be traveling wavesbecause they both travel from one point to another, as from one end of the string to the other end in Fig. 16-1 and from one end of the pipe to the other end in Fig. 16-2. Note that it is the wave that moves from end to end, not the material (string or air) through which the wave moves.

Fig. 16-1

Fig. 16-1 (a) A single pulse is sent along a stretched string. A typical string element (marked with a dot) moves up once and then down as the pulse passes. The ele-ment’s motion is perpendicular to the wave’s direction of travel, so the pulse is a transverse wave.(b) A sinusoidal wave is sent along the string. A typical string ele-ment moves up and down continuously as the wave passes. This too is a transverse wave.

Types of Waves

Waves are of three main types:

1. Mechanical waves. These waves are most familiar because we encounter them almost constantly; common examples include water waves, sound waves, and seismic waves. All these waves have two central features: They are gov-erned by Newton’s laws, and they can exist only within a material medium, such as water, air, and rock.
2. Electromagnetic waves. These waves are less familiar, but you use them constantly; common examples include visible and ultraviolet light, radio and television waves, microwaves, x rays, and radar waves. These waves require no material medium to exist. Light waves from stars, for example, travel through the vacuum of space to reach us. All electromagnetic waves travel through a vacuum at the same speed c
   299 792 458 m/s. 
3. Matter waves. Although these waves are commonly used in modern tech-nology, they are probably very unfamiliar to you. These waves are associated with electrons, protons, and other fundamental particles, and even atoms and molecules. Because we commonly think of these particles as constituting mat-ter, such waves are called matter waves. 

Much of what we discuss in this chapter applies to waves of all kinds. However, for specific examples we shall refer to mechanical waves.