17.2 - Standing waves

Standing wave: Oscillations with a stationary

outline produced by the combination of two

identical waves moving in opposite directions.

When two identical traveling waves move in opposite directions through a medium, the

resulting combined wave stays in the same location. The resulting wave is called a

standing wave. Individual particles oscillate up and down, but unlike the case of a

traveling wave, the locations of the peaks and troughs of a standing wave stay at fixed

positions.

Consider the illustration above, showing waves on a string. The standing wave is

formed by the combination of two traveling waves. We show three “snapshots” in time

of two identical waves traveling in opposite directions, and the combined wave they

create. The traveling waves are shown in colors. These waves have the same

frequency and amplitude, but are traveling in opposite directions. The result is a

standing wave that does not move along the string.

In the first snapshot above, the two traveling waves are out of phase, and they destructively interfere. The combined standing wave has a

constant zero displacement. In the second snapshot, the traveling waves have moved slightly, and the standing wave exhibits some peaks and

troughs. In the third snapshot, the traveling waves exactly coincide, in phase, to constructively interfere, and the standing wave has its largest

peaks and troughs. As the traveling waves continue to move, the standing wave’s peaks and troughs will diminish until the traveling waves are

again out of phase and the standing wave is flat.

If you find this difficult to visualize, you can see a simulation of the creation of a standing wave by clicking on the whiteboard above. You can

have the simulation move slowly, step by step, by pressing the arrow buttons. You can also press “show components” if you want to see the

component traveling waves. Press REPLAY to restart the simulation.

Along a standing wave, there are some fixed positions where there is no displacement and others where there is the maximum displacement.

The positions with no displacement are called nodes. The positions where the wave has the greatest displacement (the peaks and troughs) are

called antinodes. Adjacent nodes (and antinodes) are separated by a constant distance. Looking at the illustration for Concept 2, you can see

that two adjacent nodes are separated by one half the wavelength of the wave. The same is true for two adjacent antinodes.

The standing wave depicted above is created by the combination of transverse waves. Longitudinal waves, such as sound waves, can combine

to form standing waves as well.

Standing wave

Created by identical waves moving in

opposite directions

Standing wave

Nodes: no displacement

Antinodes: maximum displacement

(^324) Copyright 2000-2007 Kinetic Books Co. Chapter 17