Background A wave is a disturbance that carries energy, a disturbance that transports energy from one place to another without the transfer of matter. After a wave passes through a medium, there are no residual effects; the medium remains unchanged. For example, if you throw a stone in a pond, a circular wave will spread out from the point of impact. If the wave encounters an object floating in the water, the object will briefly bob up and down. However, once the wave has passed, the object, and the water that buoys it up, will be left undisturbed. We encounter waves everyday. Some are apparent; others go unnoticed. The room in which you are sitting is being criss-crossed by all sorts of waves. These include light waves, radio waves, and sound waves. While we have receptors for light and sound, our bodies are not capable of sensing radio waves directly. What travels in all waves? Energy! Energy is the quantity that travels in a wave. A wave is a disturbance that transfers energy, frequently repeating in a regular pattern. The Anatomy of a Wave Key Components In the above diagram the straight line represents the position of the medium when no wave is present. This medium could be imagined as a rope fixed at one end a few feet above the ground and held by you at the other end.
The curved line represents the position of the medium as a wave travels through it. We simply say that the curved line is the wave. Often, when several waves are traveling along a medium as shown above, the continuous group of waves is called a wave train. Crest and Trough The section of the wave that rises above the undisturbed position is called the crest. That section which lies below the undisturbed position is called the trough. These sections are labeled in the following diagram: draw Amplitude The term amplitude can have slightly different meanings depending upon the context of the situation. Its most general definition is that the amplitude is the maximum positive displacement from the undisturbed position of the medium to the top of a crest. This is shown in the following diagram: draw
In some discussions, it is important to distinguish between positive and negative amplitudes. These displacements are shown in the following diagram: Sometimes it is necessary to discuss amplitude at a certain point along the wave. Several of these amplitudes are shown in the following diagram: draw Notice in the above diagram that three of the amplitudes are positive and two are negative. Here are some other labeled examples of positive and negative amplitudes: draw
In general, if the question simply is 'What is the amplitude of the wave?', the answer follows the description of amplitude shown in the first of the above four amplitude diagrams. It is the maximum positive displacement of the medium from its undisturbed position to the top of a crest. In many discussions, though, the term amplitude takes on a slightly more complicated meaning. For example, in a discussion about wave interference the later descriptions of positive and negative amplitudes at certain points would surface. In such contexts, amplitude means the displacement of the medium from its undisturbed position to its disturbed position at a certain point along the wave. All of this becomes clear as you study waves further and understand the context of your situation. To sum up amplitude, we would say: It is the displacement of the medium from its normal position. Usually this simply means the maximum positive displacement. Often, especially in discussions about interference, amplitude means the displacement of the medium from its normal position at certain points, and this displacement can be positive or negative. Wavelength The wavelength of a wave is the distance between any two adjacent corresponding locations on the wave train. This distance is usually measured in one of three ways: crest to next crest, trough to next trough, or from the start of a wave cycle to the next starting point. This is shown in the following diagram:
Actually, the a wavelength exists between any point on a wave and the corresponding point on the next wave in the wave train. A few of such distances are shown below: Frequency is often not termed as a part of a wave, but it makes sense to introduce its meaning in this section. Frequency refers to how many waves are made per time interval. This is usually described as how many waves are made per second, or as cycles per second. The following interactive diagram lets you adjust the frequency of the wave train. (The animation may jitter a tiny bit the moment that you change frequency. This means nothing.) Some waves, such as sound and water waves, require a material medium. On the other hand, light and other forms of electromagnetic radiation can travel through the vacuum of space. Double Waves A fascinating feature of waves is that two of them, traveling in opposite directions, can pass right through each other and emerge with their original identities. However, while the pulses overlap, the height at any point is simply the sum of the displacements due to each pulse itself. If the pulses are on the same side of the medium they add; if they are on opposite sides, they subtract. This is called interference. The importance of wave phenomena in everyday life cannot be overstated. It is estimated that human beings receive over 90% of their information from light and
sound. The experiments that follow will allow you to gain first hand experience with the properties of waves in general and sound in particular. Sound is caused by small areas of high and low pressure progragating outward from the source. One convenient way to diagram a sound wave is to graph the pressure at each point in time, the way it might be picked up by a microphone for example: This simplest kind of pressure wave is called a sine wave. Interesting things to measure for a sine wave: 1. amplitude (or loudness, size of pressure differences) usually measured in decibels (db) 2. wavelength 3. frequency (or pitch) usually measured in cycles per second, or Hertz (Hz) Frequency and amplitude are independent of each other. Two sine waves may have the same frequency and different amplitudes, and vice versa. What is Sound? Sound is a type of energy made by vibrations. When any object vibrates, it causes movement in the air particles. These particles bump into the particles close to them, which makes them vibrate too causing them to bump into more air particles. This movement, called sound waves, keeps going until they run out of energy. If your ear is within range of the vibrations, you hear the sound. Picture a stone thrown into a still body of water. The rings of waves expand indefinitely. The same is true with sound. Irregular repeating sound waves create noise, while regular repeating waves produce musical notes. When the vibrations are fast, you hear a high note. When the vibrations are slow, it creates a low note. The sound waves in the diagram show the different frequencies for high and low notes.
Low frequency notes High frequency notes 1. Can sound travel under the water? Yes sound can travel under the water. It moves four times faster through water than through the air. It can travel such long distances that whales can hear each other when they are nearly a hundred miles apart. 2. Is there sound on the moon? No, there is no sound in space. Sound needs something to travel through like air or water. 3. What is the speed of Sound? Sound travels through air at 1,120 feet (340 meters) per second. Waves of light
Demonstration #1 Waves in Motion (requires two persons) Materials: Phone cord or slinky Key Concept: A wave is a disturbance that travels through a medium. Waves are characterized by wavelength, frequency, and amplitude. Waves reflect when they encounter a barrier or different medium. A rope or a long spring may be used to demonstrate many properties of waves. Hold one end of the stretched medium in your hand while your partner holds the other end. Now move one end up and down at different rates (frequencies). What happens to the wavelength as you increase the frequency? Decrease the frequency? Figure 1 Helical Spring "Snky" Does the tension in the medium have any observable effect on the speed of a wave? To find out, send a sharp pulse down the medium when the medium is under various degrees of tension. What do you observe? Send another sharp pulse down the medium. This time watch carefully as the pulse reaches the fixed end. Does the pulse reflect? If so, is the reflected pulse the same as the incident pulse or is it upside down? Do the incident and reflected pulses travel at the same speed? Stretch out the phone card across an area. Have one student come up and hold one end of the cord. Have the student hold the cord still and move your end up and down to create a standing wave. A standing wave is where one or more parts of the card do not move. You will need to find the right frequency to create a standing wave. It is fairly easy with a little practice. The Unusual Way of Waves Key Concept: The overlapping, or superposition, of two waves produces reinforcement in some instances and cancellation in others. You can witness wave interference on a phone cord, rope, or Slinky. After producing one pulse on the medium, generate a second shortly thereafter. Watch carefully as the two pulses meet and pass through one another. How would you describe the medium when the two pulses overlapped? Did the pulses produce a larger or smaller resultant pulse? What procedure must you follow to produce constructive interference (a larger net pulse)? Destructive interference (a smaller net pulse)?
Nice Nodes Key Concept: Standing waves are formed when two sets of identical waves pass through a medium in opposite directions. Move the end of the medium of choice (rope, phone cord, Slinky) up and down at the right frequency to create a full wave. When this has been accomplished you will notice that the center of the medium appears to stand still. This stationary point is called a node. At a node, the destructive interference of the incident and reflected waves is total. On either side of the node are regions of maximum displacement called antinodes. Have someone gently pinch the node with their fingers. What happens? Increase the frequency of the up and down motion of your hand until two nodes appear on the medium. How many antinodes are there now? How many wavelengths do you observe? What happens when you continue to increase the frequency of the waves? Can you obtain three nodes, four nodes, etc.? Describe what happens to the wavelength as the frequency is increased. Are You Chicken? Key Concept: A surface set in motion by a vibrating string amplifies sound. Using a toothpick, puncture a small hole in the center of the base of a paper or plastic cup. Pull a ½ meter, or so, length of string through the hole. With the cup turned upside down, tie the string around the toothpick (see figure). Rub a little rosin on your thumb and index finger. Using a jerking motion, pull down on the string while gently pinching it between the thumb and index finger. Describe what you hear as the string moves between the fingers. What is the source of the sound you hear? Why is the sound so loud? To answer this question, it may be helpful to pull on the string when it is not connected to the cup. What's it sound like?
Directions Line up eight glasses of about the same size and shape. Fill the first glass about 1/8th full of water for the high note, the second glass should be 1/4 full, the third glass should be 3/8ths full for the next note, and so on. Each glass should sound like a note on the music scale (do, re, mi, fa, sol, la, ti, do). You may need to tune your music scale (add or remove water with teaspoon) until each note rings true. Have the children use a metal teaspoon to gently tap out the scale and any other melodies they know (Mary had a Little lamb, Twinkle Twinkle). Hints for Water Chimes Don't use expensive crystal glasses to make water chimes. Add a bit a food coloring to help children identify which glass is which sound. Changing the amount of water will change the musical note. The amount of water in the glass changes the pitch of the sound wave. DO NOT TAP BOTTLES Use alcohol wipes between visitors Can you use the notes to play a simple tune?