16.1 Traveling waves  (Page 3/14)

The water wave in the figure moves through the medium with a propagation velocity $\overrightarrow{v}.$ 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

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 .

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.