9.12: Standing Waves

Standing waves are completely different from the various types of progressive waves described previously in this chapter. Standing waves are sometimes called “stationary waves” or “seiches.” Their crests and troughs alternate at fixed locations, and they do not progress across the water surface.

A simple standing wave can be produced in a rectangular cake pan partially filled with water. If you slowly lift one end of the pan a few centimeters and then set it down quickly, the water will slosh back and forth from end to end of the pan. As you tilt the pan, the water surface remains level, but as you set it down, the water must move quickly so that the surface returns toward the level position. However, the surface overruns the level position, and water continues to flow until the surface is tilted in the direction opposite the tilt that occurred when you first set the pan down. An oscillating motion of the water surface continues back and forth (Fig. 9-25a) as the wave energy is reflected off either end of the pan until friction slows and finally stops the motion. The wavelength of the standing wave equals twice the length of the pan, and a standing wave is formed rather than progressive waves because the wave is blocked by (cannot progress past) the ends of the pan.

Figure 9-25. The motion of water in standing waves. The standing-wave motion is a seesaw oscillation of the surface. Standing waves have one or more nodes (where there is no change in the water surface height but there are oscillating horizontal currents) and one or more antinodes (where there are no currents but the surface oscillates up and down). (a) A standing wave with a single node. (b) A standing wave with two nodes. (c) A standing wave that is essentially a half wave with a node at the basin entrance and only one antinode, at the closed end of the basin.

The water surface at the center of a standing wave does not move up and down. This position is called a node (Fig. 9-25). At the antinodes (Fig. 9-25), which are at the ends of the standing wave, water within the waves can move only up and down; hence, there are no horizontal currents at these antinodes. Because water must be moved from one end of the wave to the other as it oscillates, water at the node moves back and forth horizontally. The current flows in one direction at the node as the wave moves in that direction, and then reverses when the wave moves back. Horizontal or nearly horizontal reversing currents occur at all points within the wave, except at the antinodes. The maximum speed of these currents is highest at the node and decreases with distance from the node until it is zero at the antinodes.

Standing waves are important within lakes and restricted ocean basins. They form especially easily in basins with steep sides because the sides reflect wave energy and little energy is lost by friction with the seafloor. Standing waves are refracted like progressive waves. Because water moves horizontally except at the antinodes, standing waves in very large basins, such as the Great Lakes of North America, are deflected by the Coriolis effect. The influence of the Coriolis effect on a standing tide wave is examined in Chapter 10.

The standing wave just described is essentially one-half of a wave because the crest and trough of the wave are at opposite ends of the basin. Standing waves with more than one node can be established in certain basins (Fig. 9-25b).

When a progressive wave of exactly the right period arrives at the entrance to a basin of exactly the correct length, a standing wave is established in the basin. Each successive crest of the standing wave must arrive at the basin entrance at the same time that a crest of a progressive wave arrives from the other direction. This type of tuned oscillation is often important in tidal motions within enclosed bays or estuaries (Chap. 10). The oscillation is tuned in much the same way that organ pipes are tuned to specific wavelengths of air oscillations that create different musical notes. The pure note in an organ pipe is a single-node standing wave, whereas harmonics are standing waves that have two or more nodes within the pipe.