KEY CONCEPT Waves have measurable properties. BEFORE, you learned NOW, you will learn • Forces cause waves • How amplitude, wavelength, •Waves transfer energy and frequency are measured •Waves can be transverse • How to find a wave’s speed or longitudinal VOCABULARY THINK ABOUT crest p. 497 How can a wave trough p. 497 be measured? amplitude p. 497 wavelength p. 497 This enormous wave moves the frequency p. 497 water high above sea level as it comes crashing through. How could you find out how high a water wave actually goes? How could you find out how fast it is traveling? In what other ways do you think a wave can be measured? Read on to find out. Waves have amplitude, wavelength, and frequency. The tallest ocean wave ever recorded was measured from the deck of a COMBINATION NOTES ship during a storm. An officer on the ship saw a wave reach a height Use combination notes that was level with a point high on the ship, more than 30 meters in your notebook to describe how waves can (100 ft)! Height is a property of all waves—from ripples in a glass of be measured. water to gigantic waves at surfing beaches—and it can be measured. The speed of a water wave is another property that can be measured—by finding the time it takes for one wave peak to travel a set distance. Other properties of a wave that can be measured include the time between waves and the length of a single wave. Scientists use the terms amplitude, wavelength, and frequency to refer to some commonly measured properties of waves. check your reading What are three properties of a wave that can be measured? 496 Unit 4: Waves, Sound, and Light Measuring Wave Properties crest A crest is the highest point, or peak, of a wave. A trough is the lowest point, or valley, of a wave. Suppose you are riding on a boat in rough water. When the boat points upward and trough rises, it is climbing to the crest of a wave. When it points downward and sinks, the boat is falling to the trough of the wave. 1 Amplitude for a transverse wave is the distance between a line through the middle of a wave and a crest or trough. In an ocean wave, amplitude measures how far the wave rises above, or dips below, its original position, or rest position. Amplitude is an important measurement, because it indicates how much energy a wave is carrying. The bigger the amplitude, the more energy the wave has. Find amplitude on the diagram below. 2 The distance from one wave crest to the very next crest is called VOCABULARY the wavelength. Wavelength can also be measured from trough Remember to add a four square to your notebook to trough. Find wavelength on the diagram below. for each new term on this page. 3 The number of waves passing a fixed point in a certain amount of time is called the frequency. The word frequent means “often,” so frequency measures how often a wave occurs. Frequency is often measured by counting the number of crests or troughs that pass by a given point in one second. Find frequency on the diagram below. check your reading How is amplitude related to energy? Wave Properties 2 crest Wavelength is the distance from one crest or trough to the next. water level at rest fixed point 1 Amplitude is the distance a 3 medium moves Frequency is the number of waves passing a fixed above or below its trough position at rest. point in a certain amount of time. Distance above or below rest position Distance above or below rest How many wavelengths are shown in this diagram? How do you know? Chapter 15: Waves 497 How Frequency and Wavelength Are Related The frequency and wavelength of a wave are related. When frequency increases more wave crests pass a fixed point each second. That means the wavelength shortens. So, as frequency increases, wavelength decreases. The opposite is also true—as frequency decreases, low frequency, wavelength increases. long wavelength Suppose you are making waves in a rope. If you make one wave crest every second, the frequency is one wave per second (1/s). Now suppose you want to increase the frequency to more than one wave per second. You flick the rope up and down faster. The wave crests are now closer high frequency, together. In other words, their wavelengths have decreased. short wavelength Graphing Wave Properties The graph of a transverse wave looks much like a wave itself. The illustration on page 499 shows the graph of an ocean wave. The meas- urements for the graph come from a float, or buoy (BOO-ee), that reminder keeps track of how high or low the water goes. The graph shows the Frequency is the number of position of the buoy at three different points in time. These points are waves that pass a given point in a certain amount numbered. Since the graph shows what happens over time, you can of time. see the frequency of the waves. Unlike transverse waves, longitudinal waves look different from their graphs. The graph of a longitudinal wave in a spring is drawn below. The coils of the spring get closer and then farther apart as the wave moves through them. wavelength wavelength amplitude Distance between coils VISUALIZATION The shape of the graph resembles the shape of a transverse wave. CLASSZONE.COM The wavelength on a longitudinal wave is the distance from one Watch the graph of a wave form. compression to the next. The amplitude of a longitudinal wave measures how compressed the medium gets. Just as in a transverse wave,frequency in a longitudinal wave is the number of waves passing a fixed point in a certain amount of time. check your reading How are longitudinal waves measured? 498 Unit 4: Waves, Sound, and Light Graphing a Wave The graph of a transverse wave looks like a wave itself. The graph shows what happens over time. The buoy moves up and down as the waves pass. 1 Time: 0 s The buoy is 2 Time: 1 s The buoy is 3 Time: 2 s The buoy is below the rest position. equal with the rest position. above the rest position. water level at rest wavelength 0.2 3 0.1 0 2 amplitude = 0.2 m –0.1 frequency = 0.25/s 1 Distance above or below rest position (m) Distance above or below rest –0.2 01 2 34 Time (s) How many seconds does it take for one wave to pass? How much of the wave passes in one second? Chapter 15: Waves 499 Frequency SKILL FOCUS How can you change frequency? Collecting data PROCEDURE MATERIALS 1 Tie 3 washers to a string. Tape the string to the side of your desk so •3 metal washers that it can swing freely. The swinging washers can model wave action. •piece of string • tape 2 Pull the washers slightly to the side and let go. Find the frequency by • stopwatch counting the number of complete swings that occur in 1 minute. • meter stick 3 Make a table in your notebook to record both the length of the TIME string and the frequency. 30 minutes 4 Shorten the string by moving and retaping it. Repeat for 5 different lengths. Keep the distance you pull the washers the same each time. WHAT DO YOU THINK? •How did changing the length of the string affect the frequency? •How does this model represent a wave? How does it differ from a wave? CHALLENGE How could you vary the amplitude of this model? Predict how changing the amplitude would affect the frequency. Wave speed can be measured. In addition to amplitude, wavelength, and frequency, a wave’s speed can be measured. One way to find the speed of a wave is to time how long it takes for a wave to get from one point to another. Another way to find the speed of a wave is to calculate it. The speed of any wave can be determined when both the frequency and the wavelength are known, using the following formula: reminder The symbol ␭ represents Speed = wavelength • frequency wavelength. S = ␭f Different types of waves travel at very different speeds. For example, light waves travel through air almost a million times faster than sound waves travel through air. You have experienced the difference in wave speeds if you have ever seen lightning and heard the thunder that comes with it in a thunderstorm. When lightning strikes far away, you see the light seconds before you hear the clap of its thunder. The light waves reach you while the sound waves are still on their way. How fast do you think water waves can travel? Water waves travel at different speeds. You can calculate the speed using wavelength and frequency. 500 Unit 4: Waves, Sound, and Light Suppose you wish to calculate the speed of an ocean wave with a wavelength of 16 meters and a frequency of 0.31 wave per second. When working through the problem in the example below, it is helpful to think of the frequency as RESOURCE CENTER ƒ = 0.31 (wave)/s CLASSZONE.COM even though the units for frequency are just 1/second. You can think Find out more about wave speed. of wavelengths as “meters per wave,” or ␭ = 16 m/(wave) Calculating Wave Speed Sample Problem An ocean wave has a wavelength of 16 meters and a frequency of 0.31 wave per second.