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16.1 Traveling waves  (Page 3/14)

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The water wave in the figure moves through the medium with a propagation velocity v → . The magnitude of the wave velocity    is the distance the wave travels in a given time, which is one wavelength in the time of one period, and the wave speed    is the magnitude of wave velocity. In equation form, this is

v = λ T = λ f .

This fundamental relationship holds for all types of waves. For water waves, v is the speed of a surface wave; for sound, v is the speed of sound; and for visible light, v is the speed of light.

Transverse and longitudinal waves

We have seen that a simple mechanical wave consists of a periodic disturbance that propagates from one place to another through a medium. In [link] (a), the wave propagates in the horizontal direction, whereas the medium is disturbed in the vertical direction. Such a wave is called a transverse wave    . In a transverse wave, the wave may propagate in any direction, but the disturbance of the medium is perpendicular to the direction of propagation. In contrast, in a longitudinal wave    or compressional wave, the disturbance is parallel to the direction of propagation. [link] (b) shows an example of a longitudinal wave. The size of the disturbance is its amplitude A and is completely independent of the speed of propagation v .

Figure a, labeled transverse wave, shows a person holding one end of a long, horizontally placed spring and moving it up and down. The spring forms a wave which propagates away from the person. This is labeled transverse wave. The vertical distance between the crest of the wave and the equilibrium position of the spring is labeled A. Figure b, labeled longitudinal wave, shows the person moving the spring to and fro horizontally. The spring is compressed and elongated alternately. This is labeled longitudinal wave. The horizontal distance from the middle of one compression to the middle of one rarefaction is labeled A.
(a) In a transverse wave, the medium oscillates perpendicular to the wave velocity. Here, the spring moves vertically up and down, while the wave propagates horizontally to the right. (b) In a longitudinal wave, the medium oscillates parallel to the propagation of the wave. In this case, the spring oscillates back and forth, while the wave propagates to the right.

A simple graphical representation of a section of the spring shown in [link] (b) is shown in [link] . [link] (a) shows the equilibrium position of the spring before any waves move down it. A point on the spring is marked with a blue dot. [link] (b) through (g) show snapshots of the spring taken one-quarter of a period apart, sometime after the end of` the spring is oscillated back and forth in the x -direction at a constant frequency. The disturbance of the wave is seen as the compressions and the expansions of the spring. Note that the blue dot oscillates around its equilibrium position a distance A , as the longitudinal wave moves in the positive x -direction with a constant speed. The distance A is the amplitude of the wave. The y -position of the dot does not change as the wave moves through the spring. The wavelength of the wave is measured in part (d). The wavelength depends on the speed of the wave and the frequency of the driving force.

Figures a through g show different stages of a longitudinal wave passing through a spring. A blue dot marks a point on the spring. This moves from left to right as the wave propagates towards the right. In figure b at time t=0, the dot is to the right of the equilibrium position. In figure d, at time t equal to half T, the dot is to the left of the equilibrium position. In figure f, at time t=T, the dot is again to the right. The distance between the equilibrium position and the extreme left or right position of the dot is the same and is labeled A. The distance between two identical parts of the wave is labeled lambda.
(a) This is a simple, graphical representation of a section of the stretched spring shown in [link] (b), representing the spring’s equilibrium position before any waves are induced on the spring. A point on the spring is marked by a blue dot. (b–g) Longitudinal waves are created by oscillating the end of the spring (not shown) back and forth along the x -axis. The longitudinal wave, with a wavelength λ , moves along the spring in the + x -direction with a wave speed v . For convenience, the wavelength is measured in (d). Note that the point on the spring that was marked with the blue dot moves back and forth a distance A from the equilibrium position, oscillating around the equilibrium position of the point.

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Source:  OpenStax, University physics volume 1. OpenStax CNX. Sep 19, 2016 Download for free at http://cnx.org/content/col12031/1.5
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