VIBRATIONS AND WAVES

Unit Overview

This unit will introduce factors that affect wave motion, wave speed, and wave interference. The importance of waves and how vibrations are related to them will also be discussed along with water, sound and seismic waves.

Unit Review

In the previous unit, wave energy was introduced. A wave was defined as a traveling disturbance that moves energy from one location to another without transferring matter. Properties of waves and wave characteristics were discussed as well as the various types of waves, how they form, and how they carry energy.

GLOSSARY OF KEY TERMS
medium	the substance or matter that a wave moves through
seismic	vibration generated by an earthquake, explosion, or similar phenomenon and propagated within the Earth or along its surface
out of phase	when one wave passes a given point at the same time as the trough of the other wave, they become weaker
in phase	when the crests of two waves pass a given point at the same time
rogue waves	these waves are sometimes referred to as “freaks of the sea, they seem to appear out of nowhere, all of a sudden in the middle of the ocean
wave interference	the addition and subtraction of wave crests and troughs causes wave interference
earthquake	the shaking and trembling that results from the sudden movement of part of the Earth’s crust
tsunamis	giant sea waves
secondary waves	seismic waves that do not travel as fast as P waves
surface waves	the slowest moving seismic waves
primary waves	these waves travel the fastest and arrive at a given point first, before any other type of wave
seismologists	scientists who specialize in the study of earthquakes and seismic activities
seismogram	a recording of earth motion as a function of time
seismograph	an instrument that is used to detect and measure seismic waves
Mercalli scale	measures the amount of earthquake energy, not as a number, but as the amount of damage by the quake as reported by observers
Richter scale	a scale of numbers, it measures the amount of energy released during a quake and the number will be the same regardless of where it is measured

For extra practice of your key terms, click on the Key Terms Crossword Puzzle PDF File.

Waves and Vibrations

Waves transfer energy, not matter, along its path. Energy moves in waves through matter or space. Changes occur in matter when energy is transferred to it. Because energy can do work, it can move matter. The energy carried by waves is transferred to whatever stops a wave. Water and sound waves are caused when something disturbs a medium. A medium is the substance or matter that a wave moves through. Water is the medium of an ocean wave. Sound waves travel through solids, liquids, and gases (air). Earth is the medium of seismic (earthquake) waves.

Water Waves

The source of a wave is the disturbance that sets it in motion. Wind is most often the source of water waves. In the previous unit you completed an experiment with a spring toy (slinky). That particular activity introduced you to the properties of waves such as size and shape and how those waves can vary. Terms such as crest, trough, wavelength, frequency, and amplitude were introduced as properties of wave energy. Complete the following activity by observing the characteristics of waves in a wave tank:

Water Tank Waves

You will need a tall and narrow glass jar with a tight-fitting lid, cold tap water, blue food coloring, and vegetable oil.

· Fill the jar 1/3 full of cold water. Add a couple of drops of the blue food coloring. tighten the lid, and swirl the jar just enough to mix the color evenly.

· Next fill the jar to the top with vegetable oil. Screw the lid on tightly. Hold the jar horizontally and move it gently back and forth to simulate the motion of water waves.

· Then use more of a rocking motion and put more energy into the waves without changing their wavelengths and frequencies.

What happened in this activity? Did you notice a change in the amplitude of the waves as more energy was applied to them? Remember that the amplitude of a wave is related to the amount of energy put into the wave. Amplitude is not determined by a wave’s length or frequency.

Factors That Affect Wave Motion

You have observed characteristics of waves using water as the medium in which the waves transfer energy. Waves can also transfer energy through solids, liquids, and gases, as well as through empty space (vacuum). Each of the waves you study in this unit will have common characteristics that have already been identified with water waves. The characteristics are wavelength, frequency, and amplitude.

Wave Speed

To find the speed of a wave you would multiply its frequency times its wavelength:

Wave speed = frequency x wavelength

Wave speed is the velocity of a traveling wave. Remember that velocity is speed in a given direction. Wave speed is like frequency, except it applies to a wave that does not repeat. Here is an example of wave speed using an everyday object: If you have ever tried to straighten out a garden hose then you have observed wave speed. As you begin shaking the hose, you are sending waves down it. The single traveling wave travels toward the kink at a certain velocity – its wave speed.

As was previously stated, a wave is a disturbance that moves through a medium. The medium could be water, air, or even a slinky. These media are distinguished by their properties – the material they are made of and the physical properties of that material such as the density, the temperature, the elasticity, etc. These physical properties describe the material itself, not the wave. On the other hand, waves are distinguished from each other by their properties – amplitude, wavelength, frequency, etc. These properties describe the wave, not the material through which the wave moves. Only a change in the properties of the medium will cause a change in the speed.

The following activity, Wave Machine, is a demonstration of how energy can move through waves:

Wave Machine Activity

A. Obtain 1 m of 2 cm-wide un-stretched elastic, 25 plastic drinking straws, staples and stapler, and a table.

B. Take the length of elastic, 1 m, and lay it across the table.

C. Lay the 25 straws across the elastic like railroad ties at right angles to the elastic. Make sure the same length of each straw sticks out on either side. Each straw should be about a finger’s width apart on the elastic.

D. Use the stapler to carefully staple each straw in place on the elastic. Staple each lengthwise.

E. Have a partner help you with this activity. Pick the straw track up from the table and hold it between you, so that the straws are positioned vertically in the air.

F. Move the straws back and forth gently at one end. What is happening? Now do the same thing from the other end. What do you observe?

G. Now tap them more quickly. Tape the two ends at the same time in opposite directions, and then in the same direction. What happens as the waves collide?

In this activity it was easy to see the straws vibrate back and forth, but was the wave motion transmitting energy? In Question #1 record your observation. In Question #2 tell whether energy or matter moved in the wave.

Wave Interference

How do powerful water waves occur? When the crests of two waves pass a given point at the same time, they are considered “in phase” and the wave crests add to make each other stronger. If the crest of one wave passes a given point at the same time as the trough of the other wave, they become weaker. They are considered to be “out of phase” and interfere with each other. This results in less water height. If the crests of several waves come together at the same time, they are “in phase”, which results in more wave height. Water waves that are “in phase” can suddenly produce a huge wave called a rogue wave. Rogue waves have been known to reach heights of 30 meters. Rogue waves are sometimes referred to as “freaks of the sea.” They seem to appear out of nowhere all of a sudden in the middle of the ocean as the crests of several waves overlap in phase. Once the crests of the waves are out of phase, a rogue wave can disappear just as suddenly as it appeared. This addition and subtraction of wave crests and troughs is called wave interference. All waves have wave interference.

Wave interference can sometimes be considered helpful. This was discussed briefly at the end of the last unit. Strong winds can make buildings sway several meters from their original position. When this happens, the oscillating motion makes the people inside feel nauseated and disoriented. During earthquakes, the same thing can happen to buildings. Motions caused by the wind can increase the energy of the earthquake waves if they have wave interference that is “in phase.” Buildings can collapse from the increased energy from the combined motions.

Some buildings are designed to withstand earthquakes. In the past earthquake-prone buildings were designed with a safety approach that “more is better.” The designs included heavy, massive materials that were solid and inflexible. Buildings with this “approach” were able to withstand minor earthquake tremors but would sustain major damage during a major earthquake. In today’s world of technology, architects and engineers are using a different approach. They are developing both active and passive control systems that are included in the structures of buildings in earthquake regions.

Earthquake Waves

An earthquake is the shaking and trembling that results from the sudden movement of part of the Earth’s crust. When the rocks in the Earth’s crust break, earthquake waves will travel through the Earth in all directions. This causes the ground to tremble and shake. When a severe earthquake occurs, the ground may rise and fall like waves in the ocean. On occasion, loud noises may be heard coming from the ground.

The surface of the Earth is broken into pieces called tectonic plates. A theory about the Earth’s evolution has begun to emerge. This theory is named the theory of plate tectonics. The word plate refers to the moving and irregularly-shaped plates that fit together like a puzzle to form the surface layer of the Earth. These plates carry the continents and are edged by trenches and ridges. When we use the word tectonic we are referring to the branch of geology that deals with the movements that shape Earth’s crust. This theory helps to explain the Earth’s formation, movements, collisions, and destruction of the crust. This theory of plate tectonics helps us understand about earthquakes. In an earlier course, you were introduced to geological events such as earthquakes and how they result from plate motion. Because of this, we will not be discussing that topic in detail, but only in reference to earthquake wave motion or as a reference to previously learned concepts.

Scientists estimate that more than one million earthquakes occur every year. In mathematical terms, that would equal about one earthquake every thirty seconds. Many of these are so small that the Earth’s surface barely moves. However, thousands of earthquakes move Earth’s surface every year. Hundreds of earthquakes make significant changes in the features of Earth. About twenty quakes each year can cause severe changes to the surface of the Earth as well as cause serious property damage and loss of life.

Faulting is the most common cause of earthquakes. This is a break in the Earth’s surface. Energy is released during this process and the rocks continue to move until all the energy is used up. Earthquakes can also occur on the ocean floor. These produce giant sea waves called tsunamis. A tsunami can cause extensive damage in coastal areas. Tsunamis can travel at speeds of 700 to 800 kilometers per hour. As they approach coastal areas, they can reach heights of greater than 20 meters. 20 meters is about as high as a 6-story building. You saw pictures of the 2004 tsunami in a previous unit, and we will discuss tsunamis, in general, later in this unit.

Seismic Waves

As you have studied in an earlier course, some faults are located deep inside the Earth while others are close to or at the surface of the Earth. Most occur between the surface and a depth of about 700 kilometers (420 miles). The focus of an earthquake is where the rocks break apart and move. This is the underground origin of an earthquake. This is where the energy is released. Directly above the focus is the epicenter. The waves reach the epicenter first. When an earthquake occurs, the worst shaking is found at the epicenter. Earthquake waves are known as seismic waves. There are three main types of seismic waves: primary, secondary, and surface waves. Each type of wave exhibits a characteristic speed and manner of travel.

Primary waves, or P waves, travel the fastest and arrive at a given point first, before any other type of wave. These P waves can travel through solids, liquids, and gases. They are able to move through the Earth at different speeds, dependent upon the density of the material through which they are moving. They speed up as they move deeper into the Earth. P waves are commonly called push-pull waves. When P waves travel, they push particles of rock into the particles ahead of them, causing compression. The rock particles then bounce back. They hit the particles behind them that are being pushed forward. These particles move back and forth in the direction the waves are moving.

Seismic waves that do not travel as fast as P waves are called secondary waves, or S waves. These waves arrive after the P waves. They travel through solids but not through liquids and gases. Just like P waves, they speed up when they pass through denser material. Because S waves do not travel through liquids like Earth’s molten interior, they are not always recorded at all locations during an earthquake. When S waves arrive at the liquid part of Earth, they cause rock particles to move from side to side. The particles of rock move at right angles to the direction of the waves. S waves travel in a snake-like motion. This is felt as a lot of quaking.

The slowest moving seismic waves are surface waves. They are commonly called L waves. L waves travel along the ground surface. These waves are slower but highly destructive. When L waves arrive it is felt like riding on a roller coaster. L waves originate at the epicenter of a quake. These waves cause most of the damage because they bend and twist the surface of the Earth. An L wave can be compared to a ripple moving across a body of water.

The above illustration is an example of L waves. L waves are divided into two types: love and Rayleigh. A love wave moves the ground from side to side. This type of wave is particularly damaging to building foundations. Rayleigh waves move in the direction that a wave is traveling. They are like rolling ocean waves.

Love waves do not travel through water so they can only affect the surface water insofar as the side of lakes and the bays of oceans by pushing the water sideways. Rayleigh waves, because of their vertical component, can affect bodies of water such as lakes.

The height of the tallest wavy lines on a seismogram is used to calculate the earthquake’s strength, or magnitude, on the Richter scale. This scale was created in 1935 and was the creation of Charles Richter and Beno Gutenberg. This was a very important development because it provided scientists with a way to determine earthquake strength based on readings from a scientific instrument (seismograph). Before that time, scientists had to observe the quake’s strength based on their observations. Obviously, these observations were not reliable or accurate. Each individual number on the Richter scale represents an earthquake stronger than an earthquake represented by the preceding number. Each increase in number represents wave amplitude 10 times greater than the number below it. A number above 6 indicates a very destructive quake. A quake that is a 10 would be devastating. The magnitude of an earthquake is a measure of the amount of energy released. The intensity of a quake varies greatly according to the distance from the earthquake, ground conditions, and other factors. Keep in mind that intensity and magnitude are different. Intensity is based on observed effects of ground shaking on people, buildings, and natural features. Magnitude is related to the amount of seismic energy released at the epicenter of the quake. It is based on the amplitude of the earthquake waves recorded on instruments. The Richter scale is not used to express damage. The increase in wave height does not equal the increase in energy released from the quake. Actually, the energy that is released is much greater. The energy of a 7.0 earthquake is 32 times greater than the energy that is released during a 6.0 quake.

The amount of damage by an earthquake depends on various factors: quake strength, the type of soil and rock that underlies the area, population of an area, kinds of buildings in the area, and the time over which an earthquake occurs. All of these factors determine how much damage an earthquake has caused. The Richter scale looks like this:

MAGNITUDE	NUMBER PER YEAR	EFFECTS
Less than 2.5	900,000	Not usually felt
2.5 – 5.4	30,000	Very minor damage
5.5 – 6.0	500	Slight damage
6.1 – 6.9	100	Can be destructive in areas with large populations
7.0 – 7.9	20	Major earthquakes
Greater than 8.0	1 every 5 to 10 years	Total destruction

There is another type of scale used to assess earthquake damage. It is called the Mercalli scale and is an observable measure of intensity. Most measurements are not made with this scale. One difference between the two scales is that they measure different things. The Richter scale is an absolute scale. It measures the amount of energy released during a quake and the number will be the same regardless of where it is measured. The Mercalli scale is a relative measure. It measures the amount of earthquake energy, not as a number, but as the amount of damage by the quake as reported by observers. The Mercalli scale is not often reported in newspapers; however, it is often useful for seismologists.

Earthquake prediction is unpredictable. However, seismologists have identified some warning signals that help to predict quakes with greater accuracy. Quite often changes in P waves and S waves are obvious before a major earthquake hits. On other occasions, the slight tilt of the Earth can be detected. Land near a fault may be observed rising or sinking slightly. Often water levels in wells go up and down. Some scientists believe that peculiar animal behavior may be an indication of an upcoming quake.

You can make your own model of a seismograph with the following activity:

Vibrating Earth Activity

You will need 8 to 10 books, 2 or 3 rubber bands, masking tape, ruler, felt-tip pen, several metal washers (with a hole diameter of 14-15 mm), a small piece of clay, and a legal size sheet of paper.

· Stack the pile of books about 30 cm high. Secure your ruler between the top two upper books.

· Using 2 or 3 rubber bands, make a chain out of them. Place the cap of the pen on the top of the pen. Tape or hook the rubber band to the cap of the pen.

· Place the 3 or 4 metal washers on the pen about halfway up. Make a lump of clay that will hold the washers in place securely.

· Place the rubber band chain on the ruler so it will hang down and the pen tip will just touch the piece of paper. Look at your rubber band chain to see if it is too long or too short and adjust as needed. You may need to move the ruler if it is too short.

· Place the legal-sized sheet of paper under the pen. Have a partner gently shake the table as you pull the sheet of paper towards yourself. Then have your partner drop a heavy book on the table as you again pull the paper. What happened? Can you think of some other ways to make the table shake? If so, compare your seismograms to see how they are different. How are they similar?

In late December of 2004, a devastating tsunami hit the Pacific and Indian Ocean coastlines. This tsunami was caused by an earthquake that was centered approximately 155 miles from Indonesia’s capital city. This quake was registered as 9.5. The quake occurred 6 miles deep in the Pacific Ocean. Following the major quake, half a dozen aftershocks were felt that rated from a 6.0 to a 7.3 on the Richter scale. We already know that tsunamis are caused from earthquake waves that release a tremendous amount of energy, radiating out in all directions from the epicenter.

Tsunami Facts

· the word tsunami is a Japanese word meaning “harbor wave”

· can occur at any time

· can travel immense distances without a loss of potency

· the deeper the water, the faster the wave

· in deep water most of the force is below the surface

· wall of water spreads away from the center at more than 500 mph

· waves spread faster under denser material

· the wavelength may extend to more than 100 km and the period might run an hour or more

· the crests might be separated by distances of 100 m (measure of wavelength), a dozen seconds may pass between the breaking of each successive wave (measure of period)

· can gain momentum over thousands of miles

· often the first wave is not the largest

· the tsunami can be fast rising tide, single wall, or a fast falling tide, or breaking waves

· as it enters shallow coastlines, the velocity slows but the height increases

· sounds like a jet fighter landing

· the water descends like a dark wall of water

· a tsunami moves faster than a person can run

· can travel up rivers and streams

· the danger can last several hours after the first wave hits

Sound Waves

Sounds are made by objects that vibrate and cause vibrations in the air or other medium around them. The vibrations make the particles in the medium move back and forth, forming waves that travel through the medium. This is what we call sound waves. Sound waves are longitudinal waves. The particles of the medium vibrate back and forth, rather than up and down as in transverse waves. Waves are usually drawn with diagrams showing their frequency (the number of waves per second, measured in hertz) and their amplitude (the strength of the waves).

The above diagram shows sound waves. In fact, sound waves move backward and forward, not up and down, but this diagram shows their measurements more clearly.

As stated above, sound is produced when an object vibrates. The vibrating object pushes particles of the matter next to it and then causes them to compress, or squeeze together. The compressed matter then compresses the matter next to it. This compression travels through the matter as a wave of energy. Sound waves travel out in all directions away from their source. This is the same effect as waves moving away from an earthquake epicenter.

Sound does not exist in a vacuum. It needs a medium (matter) to travel through. Sound can travel at different speeds through different materials. It can travel faster through solids than through liquids. It can travel faster through a warmer medium verses a cooler medium. Below are listed some mediums and the speed of sound measured in meters per second:

MEDIUM	SPEED OF SOUND (m/s)
Steel	5960
Glass	5640
Water	1482
Air	331

The properties of sound depend upon the amplitude and frequency of the waves. Remember that amplitude is the distance a wave oscillates from its resting position. The greater the amplitude of the waves, the greater (louder) the sound will be. Frequency is the number of waves that are produced in a particular amount of time. The frequency of the waves will determine the pitch, or how low or high the sound is. The higher the frequency of a wave, the higher the pitch will be.

Sound waves travel at a speed of about 340 m/s or 760 mph on a typical day. Sound waves travel at a much slower rate than do light waves. But who determined that sound waves need a medium through which to travel? In the 1660’s, an English scientist, Robert Boyle, proved that sound waves need to travel through a medium in order to transmit sound. Boyle did an experiment using a bell placed inside a vacuum. This experiment determined that as the air was eliminated from the chamber, the bell’s sound became softer and softer until, there was no sound at all.

Isaac Newton also contributed to the knowledge of sounds waves. He discovered that the velocity of sound waves through any medium depended upon the characteristics of that particular medium. He also demonstrated that the elasticity and the density of the medium determined how fast a sound wave would travel. This discovery is similar to that of earthquake waves, isn’t it?

In a previous paragraph, the mediums and speeds of sound were listed. The speed of a particular medium depends upon several factors. Factors might include density, temperature, whether the medium is a solid or a liquid, and the elasticity of the medium. If a medium is more elastic, the sound waves will travel faster.

Here is a simple activity to see if you can feel sound vibrations: You can feel sound vibrations using a balloon and a radio. Turn on a radio and hold a balloon about 10 cm (4 in.) away from the speaker. Did the balloon vibrate? Yes it did. The vibrations of the sounds make the air in the balloon begin to vibrate. Does it change if you turn up the volume?

Unit Extensions

Suggested topics for further research:

· Isaac Newton

· Robert Boyle

· Charles Richter

· Beno Gutenberg

· John Milne

· smart buildings

· earthquakes & tsunamis

· wastequakes

Careers to explore:

· Seismologist

· architectural engineer

· Geologist

Unit Conclusion

Earthquakes release a tremendous amount of energy, which is transmitted through seismic waves. Scientists study earthquake waves so they can find new ways to predict and prepare for the next one. Sound wave transmission depends on certain properties. The intensity of sound waves is dependent on the amount of energy that is put into the vibration from which the waves originate. The more intense a sound is, the more energy it carries as it moves along.