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The Behavior of Waves
a train
Listen to the audio file and notice how the sound of the train changes. The train is a source of sound waves and as the train moves, an observer such as yourself perceives a change in the frequency of those waves, which is why the sound changes. The way you hear the train depends on whether it is approaching you or moving away from you. In this section, you will learn about why this is so. You�ll learn about some of the behaviors of waves and how they interact with each other.


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Wave Interference
More than one wave can exist at the same time at the same place. When two waves meet while traveling along the same medium, the result is called wave interference. The effects of wave interference may be constructive or destructive. In other words, two waves meeting each other may combine to increase their effect (constructive interference) or they may combine in such a way as to cancel each other out (destructive interference). Let’s look at each case separately.

Constructive interference occurs when the crest of one wave overlaps the crest of another and their individual amplitudes add together. Take a look at the two waves in this diagram and notice how their crests and troughs line up with each other. These waves are said to be "in phase" with each other.

two waves in phases
When these two waves meet, their effects will add together in an example of constructive interference to produce the combined wave seen in the next diagram. Note that if you were observing this, you would only see the combined waveform and not the original interfering waves.

constructive wave interference
Now notice the two waves in the diagram below and how they differ from the waves above. These next two waves are said to be "out of phase" because their crests and troughs do not line up. When these two waves meet, their effects cancel each other out. This is an example of destructive interference. The crest of one wave is lined up with the trough of another and they simply cancel each other out.

two wave out phase
The effect of destructive interference is shown below.

destructive wave interference
Interference is a characteristic of all wave types, whether they are water waves, sound, or light. You will learn more about interference in sound waves in the section on sound and more about light wave interference in the section on light.

Show Answer ButtonConstructive interference is sometimes called amplification. Can you explain why?

Show Answer ButtonDestructive interference is sometimes called cancellation. Can you explain why?

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Wave Interference
Standing Waves
The interference of two waves can sometimes lead to the formation of a standing wave. A standing wave, also known as a stationary wave, is one that, while constantly moving, looks like it remains in one place. It looks like the wave is standing still. Imagine, for example, that you have a string attached horizontally to some fixed point on a wall. You shake the free end of the string up and down to form a wave in the string. The wave propagates through the string until it reaches the wall (fixed point). The wall is too rigid to shake and so the wave gets reflected back to you.

You therefore have an original wave and the reflected wave moving through the same medium, but they move in opposite directions. They combine to give you a standing wave. It will look like the animation below. The original wave is in red, the reflected wave is in blue and moving in the opposite direction, and the resulting standing wave is in black.

standing wave
Notice the red dots in the animation above. These are called nodes. Nodes are places in a standing wave that remain fixed or stationary; they do not move, as you can see in the animation. Nodes represent areas of destructive interference—where one wave is canceling out the effect of the other.

The positions on a standing wave with the largest amplitudes are known as antinodes. Antinodes occur halfway between nodes and represent places where two interfering waves are always undergoing constructive interference; where the crests of the original and of the reflected waves add together to produce a combined amplified waveform.


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Wave Interference
Wave Interference and Butterfly Wings

a blue butterfly
Wave interference plays an interesting role in nature. Have you ever noticed the striking iridescent colors of butterfly wings? Butterflies get their striking colors from a natural example of constructive interference.

a close up diagram of butterfly wings Butterfly wings have multiple layers through which light is reflected. The interfering light waves undergo constructive interference to produce very intense colors.
All butterfly wings are covered by thousands of microscopic scales. Each scale is split into multiple layers separated by air. As light strikes a butterfly’s wings, it is reflected many times as it passes through the multiple layers of scales. The light waves move back and forth between the scales, interfering with each other as they do so. In this case, they undergo constructive interference and amplify each other, giving the butterfly wings colors much stronger than we normally see in nature. In fact, some butterflies have wings with colors so intense that the human eye cannot perceive them. Other butterflies, however, can perceive the overly-intense colors and this is one way that butterflies keep track of each other while making long migration journeys.


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The Doppler Effect
Another wave behavior that you will learn about in this section is the Doppler Effect. For an observer, the Doppler Effect is the perceived change in frequency and wavelength of a wave when the wave source is moving relative to the observer. It applies to all types of waves; water, light, sound, etc. In the introduction to this section you, listened to a train whistle change as the train moved from one point to another. This is an example of the Doppler Effect. You can listen to the train again, and then continue with the section to learn more about the Doppler Effect.


The Doppler Effect is named for an Austrian scientist named Christian Doppler who first proposed it in 1842. It is observed whenever the source of waves is moving with respect to an observer.


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Resonance
You will learn about three other wave behaviors, resonance, reflection, and refraction, in this section. Let’s start with resonance.

person on a swing
Imagine that you are on a playground swing. At some point, you have probably learned how to pump your legs so that you can go higher and higher on the swing. As you do this, the most important factor is your timing. When you time the pumping of your legs just right, you go higher. Specifically, you have to pump in rhythm with the natural frequency of the swing in order to get yourself higher. This phenomenon is called resonance. Resonance means to resound, or sound again, and it occurs when there is an increase in amplitude when the vibrations on an object match the object’s natural frequency.


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Reflection
The mountain in this image is beautifully reflected in the lake below it. When you shine light at a mirror, the light doesn’t travel through the mirror but is returned back to you. When you shout out with a loud voice in just the right location, you hear sound waves return in the form of your echo. This happens as the sound waves from your voice strike something like a wall. Instead of entering the wall, they move back toward you. In all of these cases, a wave (either of light or of sound) remains in one medium instead of entering a new medium. These waves are reflected. Reflection, therefore, is when a wave reaches a boundary between two media and some, or all, of that wave bounces back into the first medium.

a mountain reflected in a nearby water source
A wave may be completely or partially reflected and the type of medium involved makes the difference. For example, if you fasten a spring to a wall and send a wave along the length of the string, all the wave energy will be reflected back to you because the wall is very rigid compared to the spring. However, if the wall is replaced with a less rigid material, such as another type of spring, then some of the original wave energy will be transmitted into the new medium and the original wave will be only partially reflected.

Reflection is a phenomenon common to many wave types, including sound, light, seismic, and water waves. You will learn more about sound and light reflection in later sections of this unit.

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Refraction
The final behavior of waves that you will learn about in this section is refraction. Refraction is the change in direction of a wave due to a change in wave speed. Any type of wave, including sound, light, or water, can refract when it moves from one type of medium to another. The image below shows you an example of light refraction. The straw appears bent because of the bending of light as it moves through different media, namely air, the glass, and the water. In thicker media, like corn syrup, light travels much slower through it and refracts to a greater degree. Notice that refraction differs from reflection in that when refracted, the wave continues to move in a somewhat "forward" direction, while when reflected, the wave bounces off of the boundary between media and thus moves in a somewhat "backward" direction.

staw in a drinking glass
Water waves are refracted as they move into water of different depth and sound waves are refracted if they travel through winds or through air of uneven temperatures. In this case, parts of the sound wave travel at different speeds and cause a gradual change in direction of the sound waves overall. You will learn more about the specifics of sound and light refraction in later sections of this unit.