1.28 Wave Frequency. Chapter 1. Energy
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1 Chapter 1. Energy 1.28 Wave Frequency Define wave frequency. Identify the SI unit for wave frequency. Explain how wave frequency is related to the energy of a wave. Imagine making transverse waves in a rope, like the person in the sketch above. You tie one end of the rope to a tree or other fixed point, and then you shake the other end of the rope up and down with your hand. You can move the rope up and down slowly or quickly. How quickly you move the rope determines the frequency of the waves. What Is Wave Frequency? The number of waves that pass a fixed point in a given amount of time is wave frequency. Wave frequency can be measured by counting the number of crests (high points) of waves that pass the fixed point in 1 second or some other time period. The higher the number is, the greater the frequency of the waves. The SI unit for wave frequency is the hertz (Hz), where 1 hertz equals 1 wave passing a fixed point in 1 second. The Figure 1.60 shows high-frequency and low-frequency transverse waves. You can simulate transverse waves with different frequencies at these URLs: and ysics/waves/partsofawave/waveparts.htm Q: The wavelength of a wave is the distance between corresponding points on adjacent waves. For example, it is the distance between two adjacent crests in the transverse waves in the diagram. Infer how wave frequency is related to wavelength. A: Waves with a higher frequency have crests that are closer together, so higher frequency waves have shorter wavelengths. Wave Frequency and Energy The frequency of a wave is the same as the frequency of the vibrations that caused the wave. For example, to generate a higher-frequency wave in a rope, you must move the rope up and down more quickly. This takes more energy, so a higher-frequency wave has more energy than a lower-frequency wave with the same amplitude. You can see examples of different frequencies in the Figure 1.61 (Amplitude is the distance that particles of the medium move when the energy of a wave passes through them.) 97
2 1.28. Wave Frequency FIGURE 1.60 FIGURE 1.61 Summary Wave frequency is the number of waves that pass a fixed point in a given amount of time. The SI unit for wave frequency is the hertz (Hz), where 1 hertz equals 1 wave passing a fixed point in 1 second. A higher-frequency wave has more energy than a lower-frequency wave with the same amplitude. Vocabulary hertz (Hz): SI unit of wave frequency, where 1 hertz equals 1 wave passing a fixed point per second. wave frequency: Number of waves that pass a fixed point in a given amount of time. Practice At the following URL, use the wave simulator to make waves with various amounts of energy. Measure the frequency and wavelength of the waves, and check your measurements. Then answer the question at the bottom of the Web page. Review What is wave frequency? 2. What is the SI unit for wave frequency? 3. Assume that 10 waves pass a fixed point in 5 seconds. What is the frequency of the waves in hertz?
3 Chapter 1. Energy 4. Relate wave frequency to the energy of waves. 99
4 1.29. Wave Speed Wave Speed Define wave speed. Relate wave speed to wavelength and wave frequency. Show how to calculate wave speed. Explain how wave speed is related to the medium of a wave. Assume that you move one end of a rope up and down just once to generate a wave in the rope. How long will take the wave to travel down the rope to the other end? It depends on the speed of the wave. The Speed of a Wave Wave speed is the distance a wave travels in a given amount of time, such as the number of meters it travels per second. Wave speed (and speed in general) can be represented by the equation: Speed = Distance Time Wave Speed, Wavelength, and Wave Frequency Wave speed is related to both wavelength and wave frequency. Wavelength is the distance between two corresponding points on adjacent waves. Wave frequency is the number of waves that pass a fixed point in a given amount of time. This equation shows how the three factors are related: Speed = Wavelength x Wave Frequency In this equation, wavelength is measured in meters and frequency is measured in hertz (Hz), or number of waves per second. Therefore, wave speed is given in meters per second, which is the SI unit for speed. Q: If you increase the wavelength of a wave, does the speed of the wave increase as well? 100
5 Chapter 1. Energy A: Increasing the wavelength of a wave doesn t change its speed. That s because when wavelength increases, wave frequency decreases. As a result, the product of wavelength and wave frequency is still the same speed. At the following URL, you can see what happens to the wavelength when the frequency of a wave increases. Calculating Wave Speed from Wavelength and Wave Frequency The equation for wave speed can be used to calculate the speed of a wave when both wavelength and wave frequency are known. Consider an ocean wave with a wavelength of 3 meters and a frequency of 1 hertz. The speed of the wave is: Speed = 3 m x 1 wave/s = 3 m/s Q: Kim made a wave in a spring by pushing and pulling on one end. The wavelength is 0.1 m, and the wave frequency is 2 hertz. What is the speed of the wave? A: Substitute these values into the equation for speed: Speed = 0.1 m x 2 waves/s = 0.2 m/s Calculating Wave Frequency or Wavelength from Wave Speed The equation for wave speed (above) can be rewritten as: Frequency = Speed Wavelength or Wavelength = Speed Frequency Therefore, if you know the speed of a wave and either the wavelength or wave frequency, you can calculate the missing value. For example, suppose that a wave is traveling at a speed of 2 meters per second and has a wavelength of 1 meter. Then the frequency of the wave is: Frequency = 2m/s 1m =2 waves/s, or 2 Hz Q: A wave is traveling at a speed of 2 m/s and has a frequency of 2 Hz. What is its wavelength? A: Substitute these values into the equation for wavelength: Wavelength = 2m/s 2waves/s =1 m The Medium Matters The speed of most waves depends on the medium, or the matter through which the waves are traveling. Generally, waves travel fastest through solids and slowest through gases. That s because particles are closest together in solids and farthest apart in gases. When particles are farther apart, it takes longer for the energy of the disturbance to pass from particle to particle through the medium. At the following URL, you can watch an animation showing what happens when a wave passes from one medium to another. re=player_embedded 101
6 1.29. Wave Speed Summary Wave speed is the distance a wave travels in a given amount of time, such as the number of meters it travels per second. Wave speed is related to wavelength and wave frequency by the equation: Speed = Wavelength x Frequency. This equation can be used to calculate wave speed when wavelength and frequency are known. The equation for wave speed can be written to solve for wavelength or frequency if the speed and the other value are known. The speed of most waves depends on the medium, or the matter through which they are traveling. Generally, waves travel fastest through solids and slowest through gases. Vocabulary wave speed: How far a wave travels in a given amount of time; calculated as wavelength multiplied by wave frequency. Practice Practice calculating wave speed from wavelength and frequency by doing the problems at this URL: hysicsclassroom.com/class/waves/u10l2e.cfm Review 1. What is wave speed? 2. What is the speed of a wave that has a wavelength of 2 m and a frequency of 1.5 Hz? 3. Calculate the frequency of a wave that is traveling at a speed of 3.0 m/s and has a wavelength of 1.2 m. 4. Sound energy travels through matter in waves. Do sound waves travel faster through air or water? Explain your answer. 102
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CHAPTER 5 NATURE OF WAVES 1 Introduction to wave motion Examples of wave motion Two classes of wave: Page 1 2 Standard Terminologies for Transverse wave Describing Transverse wave Wave viewpoint Particle
yarn (1-2 meters) tape sticky notes slinky short piece of yarn or ribbon calculator stopwatch
Objective: I can identify the properties of waves and relate them to the energy they carry. Materials: yarn (1-2 meters) tape sticky notes slinky short piece of yarn or ribbon calculator stopwatch Demonstration:
5. Explain what the website means when it says Waves transfer energy, not matter.
Introduction When it comes to waves, there are so many ways that waves can be talked about. Whether we are talking about the anatomy of a wave, the different classifications of waves (and there are several!)
ENERGY OF WAVES ch.1 PRACTICE TEST
ENERGY OF WAVES ch.1 PRACTICE TEST Multiple Choice Identify the choice that best completes the statement or answers the question. 1. If a wave is traveling at a certain speed and its frequency is doubled,