UNIT D SUMMARY KEY CONCEPTS CHAPTER SUMMARY 9 Waves transmit energy. Crest, trough, amplitude, wavelength Longitudinal and transverse waves Cycle Period, frequency f 1_ T Universal wave equation v fλ Wave reflection Standing waves Resonance Parts of a wave include the crest, trough, amplitude, and wavelength. (9.1) Transverse waves and longitudinal waves are two different types of mechanical waves. (9.1) A longitudinal wave consists of rarefactions and compressions. (9.1) A cycle is a complete oscillation. (9.2) The period of a wave is the time taken for one complete oscillation. (9.2) The frequency of a wave is the number of oscillations per second. (9.2) The universal wave equation relates speed, frequency, and wavelength of a wave. (9.2) Waves undergo reflection when they meet a rigid barrier. (9.2) The principle of superposition explains constructive and destructive interference of waves. (9.3) Standing waves consist of nodes and antinodes. (9.3) Resonance and resonant frequency have both positive and negative effects on humans and the environment. (9.3) 10 Sound is a longitudinal mechanical wave. Speed of sound v sound 331.6 0.606T Range of hearing Sound intensity Sound intensity level Maximum sound intensity level Standing waves in musical instruments Fundamental frequency Overtones Harmonics Beats f beat f 1 f 2 Doppler effect v f d ( w v w v s ) f s Shock wave Sonic boom Sound is an example of a longitudinal mechanical wave. (10.1) A sound wave is a travelling disturbance of compressions and rarefactions. (10.1) The wavelength of a sound wave is the distance between successive compressions or rarefactions. (10.1) Humans can only hear sounds within a certain range. (10.1) The speed of sound depends on the spacing between particles in a medium and the stiffness of the medium. (10.1) Sound intensity is the energy per unit area that passes a point each second. (10.1) Sound intensity level is measured in decibels (db). (10.1) In Ontario, the maximum continuous sound intensity level that workers can be exposed to for 8 h is 85 db. (10.1) Standing waves in a vibrating air column can produce musical notes. (10.2) When resonance is produced in an air column closed at one end, there is an antinode at the open end. (10.2) The fundamental frequency is the lowest frequency produced by a particular instrument. (10.2) Overtones are frequencies above the fundamental frequency that may exist simultaneously with the fundamental frequency. (10.2) Overtones are called harmonics when they are whole multiples of the fundamental frequency. (10.2) Beating is the periodic pattern of constructive and destructive interference that produces a periodic change in the intensity of two combining waves. (10.2) The Doppler effect describes the increase in pitch and frequency of sounds moving towards you and the decrease in pitch and frequency of sounds moving away from you. (10.3) A shock wave is formed when an object travels through a medium at a speed equal to or greater than the speed of sound in the medium. (10.3) A sonic boom is the sound heard when a shock wave is produced. (10.3) Aircraft that travel at supersonic speeds create shock waves. (10.3) 358 Unit D Summary
UNIT D REVIEW ACHIEVEMENT CHART CATEGORIES k Knowledge and understanding t Thinking and investigation c Communication a Application Key Terms Review 1. Using your own words, define these terms, concepts, principles, or laws. c crests troughs amplitude wavelength transverse wave longitudinal wave rarefactions compressions cycle period frequency universal wave equation constructive interference destructive interference nodes antinodes standing wave resonance beat Doppler effect Key Concepts Review CHAPTER 9 2. How are the units of frequency and period similar? How are they different? k 3. The SI unit for frequency is Hz. What is one other accepted unit? k 4. The diagram below shows waves in two springs. For each of the springs, how many wavelengths are shown? k the amplitude the direction of the wave k 6. Points of zero displacement on a transverse wave have the greatest kinetic energy. Which points on a longitudinal wave have the greatest kinetic energy? k 7. What aspect of a pulse determines the amount of energy it transfers? k 8. What determines the speed at which a wave travels through a spring? k 9. You notice that a dance floor vibrates noticeably with certain dance steps but not at all with others. What important principle from physics could explain the different effect? k 10. After a fresh, heavy snowfall, the outside world seems to be unusually quiet and still. Explain why using ideas that you have learned about in this unit. k 11. What causes a standing wave in a spring? k 12. Draw a transverse wave that consists of two wavelengths. On your diagram, label the equilibrium position for the medium, a crest, a trough, the amplitude, a wavelength, and the direction of the wave velocity. Along the wavelength that you identified above, draw several vector arrows to indicate the direction of the motion of the medium. k 13. What is the relationship between frequency, wavelength, and wave velocity? k 14. Use the principle of superposition and the following two wave pulses to predict what the combined wave pulse will look like when points A and B overlap. k A Question 4 5. Sound waves travelling through air are reflected from the wall of a building. Describe how the reflection affects the speed the wavelength B Question 14 Unit D Review 359
15. Predict what will happen when the wave pulse shown below reaches the heavy rope and travels along it. Will the amplitude or phase change? Sketch your answer. k Question 15 16. Under what conditions is the amplitude of a reflected wave not inverted? k 17. What is the period of a wave that vibrates with a frequency of 40 Hz? k CHAPTER 10 18. Why does moving your finger along the string of a violin alter the note that it produces? k 19. In a 100-m race, runners are spread out over 15 m at the start line. If the starter stands to one side of the start line, in line with the runners, how much of a head start does the runner nearest the starter have compared to the runner farthest from the starter? The speed of sound is 344 m/s. k 20. What property of the sound produced by a tuning fork is affected by striking the tuning fork with different forces? What does that tell you about the relationship between the properties of the sound and the sound wave created by striking the tuning fork? k 21. In terms of the length of an open pipe, what is the longest wavelength for which resonance can occur? k 22. You are walking north along a street when a police car with its siren on comes down a side street (travelling east) and turns northward on the street in front of you. Describe what you would hear, in terms of frequency of the sound of its siren, before and after the police car turns. k 23. Why does the frequency of a sound source that is moving toward you seem to be higher than it would be if the source were at rest? k 24. Even though waves of the same frequency can interfere with each other, they will not produce beats. Why must two waves have different frequencies in order to produce beats? k 25. You have two audio frequency generators, one set at 1050 Hz and the other set at 1047 Hz. When both generators are on, how many beats would you hear in 15 s? k 26. A seal sees a shark 53.0 m away and lets out a squeal. If the speed of sound through sea water is 1533 m/s, how long will it take for the echo of the squeal to return to the seal? k 27. If the distance to the reflecting object is the same, would you hear an echo return faster on a cold day or on a hot day? Explain your answer. k 28. The speed of sound in air is 335 m/s. What is the air temperature? k 29. In what frequency range is a sound of 0.5 Hz? k 30. Your MP3 player headphones at maximum volume have a sound intensity of 10 2 W/m 2. (a) What is their sound intensity level in decibels? k (b) Use the three-decibel exchange rate to determine how long you can safely listen to an MP3 player at the sound intensity level in (a). k Connect Your Understanding 31. When a wave slows down, what property of the wave is not affected? What effect does slowing down have on other properties of the wave? Explain. k 32. Explain how a wave can transmit energy through a medium without actually transmitting any matter. k 33. If you hold a 1.00-m-long aluminium rod at its centre, it will ring with a very pure tone that has a frequency of about 2900 Hz. Estimate the speed of sound in aluminium and explain how you used the information given to do so. k 34. A string is stretched between two fixed ends 1.20 m apart. When the string vibrates with a frequency of 60 Hz, you observe a standing wave in which the nodes are separated by 0.40 m. (a) Sketch the standing wave in your notebook. k (b) From the information given, determine the speed of the wave in the string. k 35. (a) What factors affect the frequency of a vibrating string? k (b) How does each factor in (a) affect the frequency of the string? k 360 Unit D Review
36. What is the length, in wavelengths, of a string that is vibrating in its fundamental mode? k 37. The vibrating string playing an A note (440 Hz) is 33.0 cm long. How long should the segment of the same string be to produce a C note (523 Hz)? k 38. When a piano is played, describe the path of sound energy from the string to the air. k 39. What is the function of the tuning pegs on a violin? a 40. (a) How is it possible to play different notes with the same string on a guitar? a (b) Why is it more difficult to do the same thing with a violin? a 41. Write a brief procedure for a controlled experiment to determine how string diameter affects frequency. t 42. Compare and contrast playing a violin with playing a piano using a Venn diagram. t 43. If you double the distance from a sound source, its sound intensity in W/m 2 will decrease by a factor of four (assuming that no sound is absorbed over this distance). What will be the change in sound intensity level, in db? k 44. If you hold a 1.00-m-long aluminium rod at its centre, it will ring with a very pure tone. If you slide your fingers only a few centimetres to either side of the centre, the rod does not vibrate as much. Explain why this happens. t 45. A light wave is transmitted through space at 3.00 10 8 m/s. If visible light has wavelengths ranging from about 4.30 10 7 m to 7.50 10 7 m long, what range of frequencies are we able to see? a 46. Radio waves travel at the speed of light waves (3.00 10 8 m/s). If your radio is tuned to a station broadcasting at 1250 khz, what is the length of the waves arriving at the radio antenna? a 47. A pendulum oscillates with a period of 0.350 s. Attached to the pendulum is a pen that marks a strip of paper on the table below the pendulum as it oscillates. When the strip of paper is pulled sideways at a steady speed, the pen draws a sine curve on the paper. What will be the wavelength of the sine curve if the speed of the paper is 0.840 m/s? k 48. A submarine sends out a sonar wave that has a frequency of 545 Hz. If the wavelength of the sound is 2.60 m, how long does it take for the echo to return when the sound is reflected from a submarine that is 5.50 km away? k 49. A wire is stretched between two points that are 3.00 m apart. A generator oscillating at 480 Hz sets up a standing wave in the wire that consists of 24 antinodes. What is the velocity at which waves move in this wire? k 50. A spring is stretched to a length of 5.40 m. At that length, the speed of waves in the spring is 3.00 m/s. (a) If a standing wave with a frequency of 2.50 Hz were generated in this spring, how many nodes and antinodes would there be along the spring? k (b) What is the next lower frequency for which a standing wave pattern could exist in this spring? k 51. (a) In a typical adult ear, the length of the ear canal is about 26 mm. Explain why this length implies that the ear is most sensitive to sounds with frequencies around 3400 Hz. t (b) Would you expect a small child s ear to be more sensitive to higher frequencies or lower frequencies than 3400 Hz, the frequency for which adult ears are most sensitive to? Why is there a difference? t 52. The second string on a violin is tuned to the note D with a frequency of 293 Hz. This frequency is the fundamental frequency for the open string, which is 33.0 cm long. (a) What is the speed of the waves in the string? t (b) If you press on the string with your finger so that the oscillating portion of the string is 2_ 3 the length of the open string, what is the frequency of the note that is created? t 53. An audio frequency generator set at 154 Hz is used to generate a standing wave in a closedpipe resonator, where the speed of sound is 340 m/s. (a) What is the shortest air column for which resonance is heard? t (b) What is the next longer column length for which resonance is heard? t Unit D Review 361
54. A submarine s sonar emits a sound with a frequency of 875 Hz. The speed of sound in seawater is about 1500 m/s. If you measure the frequency of the sound to be 870 Hz, what is the velocity of the submarine? t 55. A police car is travelling at a speed of 144 km/h. It has a siren with a frequency of 1120 Hz. Assume that the speed of sound in air is 320 m/s. (a) If the car is moving toward you, what frequency will you hear for the siren? t (b) If the car had been moving away from you at the same speed, what frequency would you have heard? t 56. If a sound source is at rest, the frequency you hear (f d ) and the actual frequency (f s ) are equal. Their ratio equals one ( f d_ f s 1). If the sound source moves toward you at an ever-increasing speed, this frequency ratio also increases. (a) Plot a graph for the ratio of the frequencies versus the speed of the sound source as the speed of the source increases from zero to Mach 1. a (b) What is the value of the ratio when the speed of the source is Mach 1? t 57. You can create a very regular transverse wave by turning on your garden hose and then jiggling it up and down. (a) How could you use this technique to estimate the speed with which the water is flowing in the hose? a (b) If there is a sudden surge in pressure and the water speed increases by 50%, how would the distance between wave crests change? a (c) Suppose you jiggle the hose up and down two times a second and notice that you get four complete waves in the span of 6 m. Estimate the speed of the water. a 58. A string is stretched between two fixed points that are separated by 2.0 m. If the string is plucked, it will vibrate as a standing wave with a node at each end at a frequency of 100 Hz. (a) Determine the wavelength of the standing wave. t (b) Find the speed of the wave in the string. t 59. If you increase the tension in the string in question 58, the wave speed will increase. Which value will change when the speed increases: the wavelength or the frequency of the standing wave? Explain. t 60. Answer the following questions about wave interference. (a) What happens when the trough of a wave meets the crest of another wave? k (b) What happens when two wave crests meet? k (c) Two vibrating sources, A and B, create waves of wavelength 12 cm. You are situated 24 cm from source A and 18 cm from source B and are receiving waves from both sources. Describe the resulting wave disturbance that you will detect from both sources. k Skills Practice 61. Use a graphing calculator or another suitable means to plot a graph of period against frequency. What type of relationship is this? k 62. Explain to someone who has not studied physics the differences in the ways objects and waves transport energy between points in Earth. k Revisit the Big Ideas and Fundamental Concepts 63. A tsunami is a potentially deadly water wave created by earthquakes and capable of travelling at speeds of over 1000 km/h. To provide ample warning to people, governments around the world have invested in tsunami warning systems. Suppose a massive earthquake occurs on the west coast of British Columbia, 1800 km from Vancouver. If the warning system issues an alert within five minutes of the event, how much warning time will Vancouver receive? a Science, Technology, Society, and the Environment 64. You can estimate your distance from a lightning storm by watching for a lightning flash and then counting in one-second intervals using the general rule that you are 1 km away for every 3 s you count. (a) Explain why this rule works. a (b) Estimate the distance from a lightning storm if it takes 8 s for the sound of the thunder to reach you after you see a flash of lightning. a 362 Unit D Review
65. The photo on the right shows a wave front travelling in front of a barge moving through a canal. What causes this phenomenon? (Hint: How would knowing the speed of the boat through water compared to the speed of the surface waves help you to answer this question?) t Reflection 66. Identify a concept or issue that you studied in this unit and that you would like to learn more about. c 67. Learning often requires that we change the way we think about things. Which concept in this unit required the greatest change in your thinking about it? Explain how your thinking changed. c Question 65 68. Which of the concepts in this unit was most helpful in explaining to you how objects interact? c D11 Unit Task PHYSICS SOURCE Does Acoustic Range of Hearing Change with Age? Question What is your acoustic range and how does it change as you grow older? Task Overview In this task, you will use a sound frequency generator to measure the range over which you are able to hear sound. You will measure the lowest and highest frequencies that you can hear. You will then measure the lowest and highest frequencies that some of your classmates can hear, and compare your data. Next, you will measure the frequency range of people in their thirties and older. The greater the number of people from different age groups you can measure, the better. The second part of your task will be to see if acoustic range changes as you age. You will need to keep accurate and well-organized records and devise a way in which to display the results of your frequency range measurements. Your teacher will provide you with a complete task description. Figure 10.43 Unit task setup Unit D Review 363