Subsequent standing waves are called the second harmonic, third harmonic, etc. The simplest of the harmonics is called the fundamental or first harmonic. The set of all possible standing waves are known as the harmonics of a system. In the case of the telephone cord, small motions in the hand result will result in much larger motions of the telephone cord.Īny system in which standing waves can form has numerous natural frequencies. Compared to traveling waves with the same amplitude, producing standing waves is relatively effortless. Resonance can be identified by a dramatic increase in amplitude of the resultant vibrations. Standing waves are always associated with resonance. That is, when the driving frequency applied to a system equals its natural frequency. They require that energy be fed into a system at an appropriate frequency. Standing waves don't form under just any circumstances. The interference of these two waves produces a resultant wave that does not appear to move. In a bounded medium, standing waves occur when a wave with the correct wavelength meets its reflection. In general, standing waves can be produced by any two identical waves traveling in opposite directions that have the right wavelength. (Or is it the other way around?) Other simple examples of finite media are a guitar string (it runs from fret to bridge), a drum head (it's bounded by the rim), the air in a room (it's bounded by the walls), the water in Lake Michigan (it's bounded by the shores), or the surface of the Earth (although not bounded, the surface of the Earth is finite). A phone cord begins at the base and ends at the handset. Standing waves can form under a variety of conditions, but they are easily demonstrated in a medium which is finite or bounded. There are also regions where the disturbance is quite intense, greater than anywhere else in the medium, called antinodes. Standing waves don't go anywhere, but they do have regions where the disturbance of the wave is quite small, almost zero. Traveling waves have high points called crests and low points called troughs (in the transverse case) or compressed points called compressions and stretched points called rarefactions (in the longitudinal case) that travel through the medium. If you shake the phone cord in any other way you'll get a wave that behaves like all the other waves described in this chapter waves that propagate - traveling waves.
If you shake the phone cord in just the right manner it's possible to make a wave that appears to stand still. I first discovered standing waves (or I first remember seeing them) while playing around with a phone cord. A traveling wave in action A standing wave in action