## Waves

The purpose of this brief section is to provide some background information that will be useful later. So, here we go:

A wave is an oscillating disturbance. Waves transmit energyEnergy will be defined in the next chapter. from one place to another without requiring matter to travel across the intervening distance. Most waves travel through a medium—a physical thing like air, water, a slinky spring, or a rope—that oscillates as the wave goes by. (Light waves apparently do not require any medium, however, as we’ll see in chapter 6.)

There are basically two types of waves:

1. In a longitudinal wave, the oscillations are parallel to the direction of the wave’s travel. (Example: sound waves)
2. In a transverse wave, the oscillations are perpendicular to the direction of the wave’s travel. (Examples: vibrating instrument strings, waves that travel along a rope)
3. Technically, there are three types of waves, but I’m going to pretend that surface waves (e.g. water waves) belong in the category of transverse waves. The distinction between transverse waves and surface waves isn’t important for my purposes.

Transverse waves (but not longitudinal waves) can be polarized, which means that the wave’s oscillations are oriented in a particular way. A wave is linearly polarized if the oscillations go back and forth in just one direction (which must be perpendicular to the wave’s direction of travel, since we’re talking about transverse waves). A wave is circularly polarized if the crest of the wave rotates around the axis of the wave’s travel.

The speed at which a wave travels is equal to its wavelength times its frequency: speed = wavelength × frequency

Wavelength is the distance between crests of a transverse wave, or between the maximally compressed parts of a longitudinal wave.

Frequency is the rate of oscillation, i.e. the number of oscillations that occur each second at a given point along the wave’s path as the wave travels by. (The standard unit of frequency is hertz, symbolized “Hz.” 1 Hz = 1 cycle per second.)

Amplitude is the height of the crest above neutral position (in a transverse wave), or the degree of compression (in a longitudinal wave).

The points of minimum amplitude (i.e. the points between peaks and troughs) are called nodes. The distance between nodes is equal to half the wavelength.

When waves meet, their oscillations may interfere with each other. Constructive interference occurs where the crests or troughs of the two waves coincide, resulting in a wave of even larger amplitude. Destructive interference occurs where the crests of one wave coincide with the troughs of the other, reducing the total amplitude or even cancelling the wave altogether. The Doppler Effect When an ambulance isn’t moving, its siren emits sound waves with the same frequency in all directions. But the sound in front of a moving ambulance has a shorter wavelength than the sound behind it, because the ambulance is moving with respect to the air. An observer on the sidewalk hears the siren change pitch (frequency) from high to low as the ambulance speeds past. Animation adapted from this video by EICC, Creative Commons license CC BY 3.0

The frequency of a wave seems to change if you are in motion with respect to the medium through which the wave is travelling. For example, water waves travel with a constant speed across the surface of a lake; so if you’re bobbing across the lake on a boat, you’ll feel the waves with lower frequency when your boat is moving the same direction as the waves, and you’ll feel them with higher frequency when your boat is moving the opposite direction. Likewise, if you drive your car quickly past a noisy block party, the pitch (frequency) of the blaring music will seem to change from higher to lower as you approach and then recede from the source of the sound.

A similar effect also occurs when the source of a wave is in motion with respect to the wave’s medium. The oscillations ahead of the moving source will have shorter wavelength and higher frequency than the oscillations behind it. For example, if you are standing on the sidewalk while an ambulance goes by, the sound of the siren has a higher pitch (higher frequency) as the ambulance approaches and a lower pitch (lower frequency) as it speeds away.

This phenomenon (shifts in frequency due to the motion of either the observer or the wave source) is called Doppler shift or the Doppler effect. When the Doppler effect occurs with light waves, it is called redshift or blueshift, because with visible light the effect results in an apparent change of color, either toward the red (lower frequency) or blue (higher frequency) side of the color spectrum.