Light, or radiation, can be thought of as a wave. As we shift across the electromagnetic spectrum, we find light of many wavelengths. Gamma-rays, x-rays, and ultraviolet radiation are all forms of light with a great deal of energy, and shorter wavelengths than those that we can detect with our eyes. The intermediate wavelengths (4000 to 7500 Angstroms) are the wavelengths of visual light, followed by infrared (heat), radio, and even gravitational radiation.

The defining characteristics of waves are that they are periodic (the pattern repeats), and they have a certain amplitude (the height of the pattern) and frequency/wavelength (the number of times the patter is repeated per unit time/the spatial length of the pattern). Think about an example of waves in our daily lives, such as sound waves (density or pressure waves) from musical instruments, waves passing along a slinky or a jump rope (transverse waves), or ocean waves (gravity or surface waves).

• When you blow along the edge of a bottle, you create a deep, resonant sound (like a foghorn). If you change the length of the bottle, either by getting a shorter/longer bottle or by filling your original bottle with water, you can change the pitch of the sound. This is the principle behind musical instruments.

• Short instruments (like a flute) produce high pitched, high frequency sound waves. The flautist changes the pitch of the sound by opening or closing off holes along the length of the flute, making it into a pipe which is shorter (high pitches) or longer (low pitches).

• Longer instruments, like a trombone, produce low pitched, deep, low frequency sound waves. The trombonist changes the pitch of the sound by contracting or extending the slide, an extra tube within the body of the instrument, making it into a tube which is shorter (high pitches) or longer (low pitches).

• Consider the following thought experiment. A musician changes the pitch of sounds to create music. In a simple case, a guitarist moves his finger along the length of a guitar string to change the frequency (pitch) of the music. As his finger moves closer and closer to one end of the string, the frequency of the sound wave rises. Now imagine that he moves his finger extremely close to one end of the string, so close that the resulting frequency moves out of the regime of sound waves ... and into the regime of visual light (higher frequencies). In a metaphorical fashion, the musician could transform sound into light!

• The speed of sound in air (on a cool day) is ~1000 feet/second. (In comparison, the speed of light is 186,000 miles/second. This is how you can estimate how far away lightning strikes are, by counting the time between seeing the lightning strike and hearing the thunder reach you.) Do the air molecules travel at this speed? In a higher-density medium (for example, railway tracks) a sound wave travels faster. In a lower-density medium, it is harder to transmit sound, and it travels slower. How does this affect astronauts doing walk-about missions in space – can they talk to each other easily?

• If you hold a slinky between your hands, with your hands far apart from each other, you can pass a low frequency, low energy wave along its surface. You are not actually moving the entire slinky from hand to hand; instead, a wave shape passes along the body of the slinky as you shake it gently. As you shake the slinky faster, putting more energy into the system, you can increase the frequency of the wave that you create (the pulses are closer together).

• Resonance: A system can build up enormous amounts of energy, if you drive it at the resonant frequency. Think about pushing a toddler on a swing at the park; she swings back and forth, back and forth, and needs constant pushing or she will slowly lose energy and the swing will stop. If you push inefficiently, at a random point in her path or not always in the direction of motion, you will work hard, occasionally get hit in the head by a loose shoe, and she will not swing very fast. If you always push her at one peak of her path, and always push in the direction of travel, you will be driving the swing at resonance and she will swing pretty quickly – perhaps fast enough to fly over the supporting bar!

• Have you heard of the 1940 Tacoma Narrows Bridge disaster? What role did waves play in amplifying the resonant effect of the 40 mph winds on the bridge, and shaking it apart?

  Normal state	Excited state
  Before, and after. [M. Ketchum]

  Just as I drove past the towers, the bridge began to sway violently from side to side. Before I realized it, the tilt became so violent that I lost control of the car. I jammed on the brakes and got out, only to be thrown onto my face against the curb. Around me I could hear concrete cracking. I started to get my dog Tubby, but was thrown again before I could reach the car. The car itself began to slide from side to side of the roadway. On hands and knees most of the time, I crawled 500 yards or more to the towers. My breath was coming in gasps; my knees were raw and bleeding, my hands bruised and swollen from gripping the concrete curb. Toward the last, I risked rising to my feet and running a few yards at a time. Safely back at the toll plaza, I saw the bridge in its final collapse and saw my car plunge into the Narrows. – Leonard Coatsworth, involuntary eye-witness

  Twisting	Tilting	Warping	Sagging	Aftermath
  The stress modes imposed on the Tacoma Narrows Bridge in 1940. [M. Ketchum]

• We understand more about the dangers of resonant effects today than in the past. But consider the Koror-Babeldaob Bridge, 800 feet in length, which collapsed suddenly one evening in 1996 after bearing loads without signs of trouble for almost thirty years.

  Palau [an archipelago located midway between Japan and Australia] is very small. A single road connects the four islands that host most of the country's 17,000 people. Between three of the islands there are raised concrete causeways; the largest island, Babeldaob, connects to Koror, the capital, by a bridge. Until recently at least. In September, 1996, the bridge – an 800-foot concrete span – fell into the channel. When I asked a local woman what had happened to it she said, It collapse. Earthquake? I asked. No, just collapse, she said, as though these things just happen sometimes. – American visitor.

  The Palau concrete bridge, before (top row) and then after (bottom row) the 1996 disaster. [M. Ketchum]