Benchmarks SC.A.2.3.1 (pp. 185, 188 191): The student describes and compares the properties of particles and waves; SC.B.1.3.6 Annually Assessed (pp. 188 191, 193): knows the properties of waves ; SC.C.1.3.2 Annually Assessed (p. 186): knows that vibrations in materials set up wave disturbances that spread away from the source. Also covers: SC.H.1.3.4 Annually Assessed (p. 193), SC.H.1.3.5 Annually Assessed (p. 193), SC.H.2.3.1 (pp. 186, 188) Waves Explain how waves transport energy. Distinguish among transverse, compressional, and electromagnetic waves. Describe the properties of waves. Describe reflection, refraction, and diffraction of waves. Devices such as televisions, radios, and cell phones receive and transmit information by waves. Review Vocabulary energy: the ability to do work or cause change New Vocabulary wave wavelength frequency amplitude law of reflection refraction diffraction What are waves? When you float in a pool on a hot summer day, the up-anddown motion of the water tells you waves are moving past. You can see water waves and feel their motion, but there are other types of waves. Sound and light waves enable you to see and hear. It is the waves produced during an earthquake that cause so much damage to buildings. Waves Transfer Energy, not Matter A wave is a disturbance that moves through matter or space. Waves, like the water waves shown in Figure 1, transfer energy from place to place. When a wave moves, it may seem that matter moves along with the wave. However, a wave transfers energy without transferring matter from one place to another. The movement of the fishing bob in Figure 1 transfers energy to water molecules. This energy is passed from one water molecule to a neighboring water molecule to yet another water molecule continuously as the wave travels outward. The wave disturbance causes water molecules to move only a short distance. Vibrating Objects Make Waves The up-and-down motion of the fishing bob in Figure 1 made the water waves that spread outward and moved away. Plucking a guitar string causes the string to vibrate back and forth, making a sound. Waves are produced by objects that are vibrating. It is the energy of the vibrating object that waves transfer outward. FCAT Vocabulary The energy transferred by ocean waves can break rocks. The movement of the fishing bob produces water waves that transfer energy through the water. Figure 1 Waves transfer energy from place to place without transferring matter. 186 CHAPTER 7 Waves, Sound, and Light (l)david W. Hamilton/Getty Images, (r)ray Massey/Getty Images
Types of Waves Sound waves travel through air to reach your ears, but they cannot travel through the empty space between Earth and the Sun. Waves that can travel only in matter and not through space are mechanical waves. Other waves, called electromagnetic waves, can travel through both matter and space. Crest Rest position Transverse Waves One type of mechanical wave is a transverse wave. A transverse wave causes particles in matter to move at right angles to the direction in which the wave travels. Figure 2 shows a transverse wave on a rope. The position of the rope before the wave starts moving is called the rest position of the rope. The rest position in any material is the position of the particles in the material before a wave starts moving. These particles return to the rest position after the wave passes. High points in the wave are called crests. Low points are called troughs. The series of crests and troughs forms a transverse wave. The crests and troughs travel along the rope, but the particles in the rope move only up and down. Trough Direction wave moves Direction rope moves Figure 2 You make a transverse wave when you shake the end of a rope up and down. Particles in the rope move at right angles to the motion of the wave. Compressional Waves Another type of mechanical wave is a compressional wave. Figure 3 shows a compressional wave traveling along a spring coil. A compressional wave causes particles in matter to move back and forth along the same direction in which the wave is traveling. In Figure 3, the place where the coils are squeezed together is called a compression. The places where the coils are spread apart are called rarefactions. A series of compressions and rarefactions forms a compressional wave. The compressions and rarefactions travel along the spring, but the coils move only back and forth. How does matter move in a compressional wave? Movement of coil Movement of wave Figure 3 A wave on a spring coil is an example of a compressional wave. Rarefaction Compression SECTION 1 Waves 187
Seismic waves are mechanical waves that move through the ground during an earthquake. Some of these waves are compressional, and others are transverse. The seismic waves that cause most damage to buildings are a kind of rolling wave. These rolling waves cause the ground to move up and down, as well as back and forth. Electromagnetic Waves Light, radio waves, and X rays are examples of electromagnetic waves. Just like waves on a rope, electromagnetic waves are transverse waves. However, electromagnetic waves contain electric and magnetic parts that vibrate up and down perpendicular to the direction the wave travels. FCAT FOCUS Annually Assessed Benchmark Check SC.C.1.3.2 How does the frequency of a wave on a rope change if the end of the rope moves up and down more quickly? Figure 4 The wavelength of a transverse wave is the distance from crest to crest or from trough to trough. The wavelength of a compressional wave is the distance from compression to compression or rarefaction to rarefaction. Properties of Waves Waves have properties that depend on the vibrations that produce the wave. For example, the faster you shake the end of a rope up and down, the closer the crests and troughs are. If you shake the end of the rope by moving it up and down a greater distance, the crests become higher and the troughs become deeper. The distance between any point on a wave and the nearest point just like it is the wavelength. Figure 4 shows the wavelengths of a transverse wave and a compressional wave. is measured in units of meters (m). The wavelength of a transverse wave is the distance between two adjacent crests or two adjacent troughs. The wavelength of a compressional wave is the distance between two adjacent compressions or rarefactions. Frequency The frequency of a wave is the number of wavelengths that pass by a point each second. The SI unit for frequency is the hertz, abbreviated Hz. One hertz equals one vibration per second or one wavelength passing a point in one second. A frequency of 5 Hz means that five wavelengths pass by in one second. The unit Hz also is the same as the unit 1/s. Rest position 188 CHAPTER 7 Waves, Sound, and Light
Amplitude of a Transverse Wave For a transverse wave, the height of the crests and the Amplitude depth of the troughs is related to a wave property called amplitude. The amplitude of a wave is the maximum distance that matter moves as the wave passes. For a transverse wave, Trough the amplitude is the distance from the top of a crest or the bottom of a trough to the rest position of the material, as shown in Figure 5. Just like the wavelength and frequency of a wave, the amplitude depends on the vibrations that produce the wave. What is the amplitude of a wave? Crest Amplitude Rest position Figure 5 The amplitude of a transverse wave is the distance from the top of a crest or the bottom of a trough to the rest position. Amplitude of a Compressional Wave The amplitude of a compressional wave depends on the density of material in compressions and rarefactions as shown in Figure 6. Compressional waves with greater amplitude have compressions that are more squeezed together and rarefactions that are more spread apart. In a spring, squeezing some coils together more tightly causes the nearby coils to be more spread apart. Amplitude and Energy The vibrations that produce a wave transfer energy to the wave. The larger the amplitude of a wave, the more energy the wave carries. By shaking the end of a rope up and down a greater distance, you increase the wave s amplitude and transfer more energy to the rope. Vibrations in Earth s crust produce seismic waves that travel on Earth s surface during earthquakes. The larger the amplitude of these waves, the more energy they carry and the more damage they cause. This compressional wave has a larger amplitude. Figure 6 The amplitude of a compressional wave depends on the density of the material in the compressions and rarefactions. This compressional wave has a smaller amplitude. SECTION 1 Waves 189
Wave Speed Waves are described by their frequency, wavelength, and amplitude. Another property of waves is speed. How fast do waves travel? The speed of a wave depends on the material in which the wave travels. The wavelength, frequency and speed of a wave are related. Using the equation below, you can calculate the wavelength of a wave if the wave speed and frequency of the wave are known. wavelength (in m) w ave speed ( in m/ s) frequency ( in Hz) v f In this equation, v is the symbol for wave speed and f is the symbol for frequency. The wavelength is represented by the Greek letter lambda,. Solve a Simple Equation WAVELENGTH OF SOUND A sound wave produced by a lightning bolt has a frequency of 34 Hz and travels at a speed of 340.0 m/s. What is the wavelength of the sound wave? Solution This is what you know: wave speed: v 340.0 m/s frequency: f 34 Hz This is what you need to find: This is the procedure you need to use: Check your answer: wavelength:? m Substitute the known values for wave speed and frequency into the wavelength equation and calculate the wavelength: v f 34 0.0 m/s 34 Hz 10.0 m / H s z 10.0 m / s 1/ 10.0 m s Multiply your answer by the frequency. The result should be the given wave speed. 1. If the frequency of a sound wave in water is 15,000 Hz, and the sound wave travels through water at a speed of 1,500 m/s, what is the wavelength? MA.D.2.3.2 2. Waves on a string have a wavelength of 0.55 m. If the frequency of the waves is 6.0 Hz, what is the wave speed? MA.D.2.3.2 Math Practice For more practice, visit fl7.msscience.com 190 CHAPTER 7 Waves, Sound, and Light
Waves Can Change Direction Waves don t always travel in a straight line. You see your reflection in a mirror because the mirror makes light waves change direction. Waves also can change direction when they travel from one material to another. Waves can reflect (bounce off a surface), refract (bend), or diffract (bend around an obstacle). r Normal i The Law of Reflection When waves reflect off a surface, they always obey the law of reflection, as shown in Figure 7. A line that makes an angle of 90 degrees with a surface is called the normal to the surface. According to law of reflection, the angle that the incoming wave makes with the normal equals the angle that the outgoing wave makes with the normal. Figure 7 All waves obey the law of reflection. The angle of reflection, r, always equals the angle of incidence, i. Refraction The speed of a wave depends on the properties of the material through which it travels. A light wave travels through air faster than it does through water. Figure 8 shows that a change in a wave s speed changes the direction in which the wave travels. As the light wave moves from air to water, it slows down. This change in speed causes the light wave to bend. Refraction is the change in direction of a wave when it changes speed as it travels from one material to another. Figure 8 Refraction occurs when a wave changes speed. Light waves change direction when they slow down as they pass from air to water. FOCUS FCAT Annually Assessed Benchmark Check SC.B.1.3.6 If the frequency of the light waves doesn t change as they slow down in moving from air into water, how does their wavelength change? SECTION 1 Waves 191 Richard Megna/Fundamental Photographs
Diffraction Waves can change direction by diffraction, which is the bending of waves around an object. In Figure 9, the obstacle does not completely block the water waves. Instead the waves bend around the obstacle. The amount of diffraction or bending of the waves depends on the size of the obstacle. If the obstacle is much larger than the wavelength, very little diffraction occurs. Then there is a shadow behind the object where there are no waves. As the wavelength increases compared with the size of the obstacle, the amount of diffraction increases. The amount of diffraction is greatest if the wavelength is much larger than the obstacle. Figure 9 The amount of diffraction, or bending around an obstacle, depends on the size of the obstacle and the wavelength of the wave. Particles and Waves Particles of matter and waves have different properties. Particles have mass and volume, and can have an electric charge. Waves have wavelength, frequency, and amplitude. Nevertheless, moving particles and waves both transport energy from one place to another. Summary Wave Energy Waves transport energy but not matter. Types of Waves Transverse waves cause particles in a material to move back and forth at right angles to the direction the waves travel. Compressional waves cause particles in a material to move back and forth along the same direction the waves travel. Electromagnetic waves are transverse waves that can travel through empty space. Wave Properties Four properties of a wave are wavelength, frequency, amplitude, and speed. The energy carried by a wave increases as the amplitude of the wave increases. The wavelength of a wave,, equals its wave speed, v, divided by its frequency, f: v f Reflection, refraction, or diffraction can cause waves to change direction. Self Check 1. Analyze How can waves transport energy without transporting matter from one place to another? 2. Explain how the spacing between coils of a spring changes as the amplitude of a compressional wave traveling along the spring increases. SC.A.2.3.1 SC.B.1.3.6 3. Predict how the wavelength of waves traveling with the same speed would change if the frequency of the waves increases. SC.B.1.3.6 4. Apply Two similar-sized stones, one heavy and one light, are dropped from the same height into a pond. Explain why the waves produced by the heavy stone have higher amplitude than the waves produced by the light stone. SC.B.1.3.6 5. Think Critically Water waves produced by a speed boat strike a floating inner tube. Describe the motion of the inner tube as the waves pass by. SC.C.1.3.2 6. Calculate Wave Speed Find the speed of a wave with a wavelength of 0.2 m and a frequency of 1.5 Hz. 7. Calculate Find the wavelength of a wave with a speed of 3.0 m/s and a frequency of 0.5 Hz. MA.D.2.3.2 MA.D.2.3.2 192 CHAPTER 7 Waves, Sound, and Light Richard Megna/Fundamental Photographs More Section Review fl7.msscience.com