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Transverse, Longitudinal

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 pulse travels along the string, as in Figure (a). 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. So, as each section moves upward in turn, it beings to be pulled back downward by neighboring sections that are already on the way down. The net result is that a distortion in the string’s shape (the pulse) moves along the string at some velocity v.

   Figure-(a) Single pulse through a string
(b) Continuous pulses through a string

Because the oscillations of any string element (represented here by a dot) are perpendicular to the direction in which the wave moves, the wave is a transverse wave.

If you move your hand up and down in continuous simple harmonic motion, a continuous wave travels along the string at velocity v. Because the motion of your hand is a sinusoidal function of time, the wave has a sinusoidal shape at any given instant, as in Figure (b). That is, the wave has the shape of since 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 assume 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 figure is to monitor the wave form (shape of the wave) as it moves to the right. Alternatively, we can monitor the motion of an element of the string as the element oscillates up and down while the wave passes through it. We would find that the displacement of every such oscillating string element is perpendicular to the direction of travel of the wave, as indicated in figure. This motion is said to be transverse, and the wave is said to be a transverse wave.

Figure (c) 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 somewhat farther along the pipe. Once they have moved rightward, the elements move back leftward. Thus the motion of the air and the change in air pressure travel rightward along the pipe as a pulse.

Figure (c) A sound wave is set up in an air-filled
pipe by moving a piston back and froth.

Because the oscillation of an element of the air (represented by the black dot) is parallel to the direction in which the wave travels, the wave is a longitudinal wave.

If you push and pull on the piston in simple harmonic motion, as is being in figure (c), 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.


Both a transverse wave and a longitudinal wave are said to be traveling waves because the wave travels from one point to another, as from one end of the string to the other end in figure (a) or from one end of the pipe to the other end in figure (c). Note that it is the wave that moves between the two points and not the material (string or air) through which the wave moves.

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