13. 16.1.1. A transverse wave is traveling along a Slinky. The drawing below represents a section of the Slinky at one instant in time. The direction the wave is traveling is from left to right. Two segments are labeled on the Slinky. At the instant shown, which of the following statements correctly describes the motion of the particles that compose the Slinky in segments A and B? a) In segment A the particles are moving downward and in segment B the particles are moving upward. b) In segment A the particles are moving upward and in segment B the particles are moving upward. c) In segment A the particles are moving downward and in segment B the particles are moving downward. d) In segment A the particles are moving upward and in segment B the particles are moving downward. e) In segment A the particles are moving toward the left and in segment B the particles are moving toward the right.
14. 16.1.2. Mike is holding one end of a Slinky. His hand moves up and down and causes a transverse wave to travel along the Slinky away from him. Is the motion of Mike’s hand a wave? a) Yes, the motion of Mike’s hand is a wave because it moves up and down in periodic motion. b) Yes, the motion of Mike’s hand is a wave because Mike is transferring energy to the Slinky. c) No, the motion of Mike’s hand is not a wave because there is no traveling disturbance. d) No, the motion of Mike’s hand is not a wave because there is no energy traveling along the Slinky.
17. Parts of a Wave Periodic waves consist of cycles or patterns that are produced over and over again by the source. In the figures, every segment of the slinky vibrates in simple harmonic motion, provided the end of the slinky is moved in simple harmonic motion.
19. Example 1 The Wavelengths of Radio Waves AM and FM radio waves are transverse waves consisting of electric and magnetic field disturbances traveling at a speed of 3.00x10 8 m/s. A station broadcasts AM radio waves whose frequency is 1230x10 3 Hz and an FM radio wave whose frequency is 91.9x10 6 Hz. Find the distance between adjacent crests in each wave. AM FM
20. 16.2.1. Jimmy and Jenny are floating on a quiet river using giant doughnut-shaped tubes. At one point, they are 5.0 m apart when a speed boat passes. After the boat passes, they begin bobbing up and down at a frequency of 0.25 Hz. Just as Jenny reaches her highest level, Jimmy is at his lowest level. As it happens, Jenny and Jimmy are always within one wavelength. What is the speed of these waves? a) 1.3 m/s b) 2.5 m/s c) 3.8 m/s d) 5.0 m/s e) 7.5 m/s
21. 16.2.2. The drawing shows the vertical position of points along a string versus distance as a wave travels along the string. Six points on the wave are labeled A, B, C, D, E, and F. Between which two points is the length of the segment equal to one wavelength? a) A to E b) B to D c) A to C d) A to F e) C to F
22. 16.2.3. A longitudinal wave with an amplitude of 0.02 m moves horizontally along a Slinky with a speed of 2 m/s. Which one of the following statements concerning this wave is true? a) Each particle in the Slinky moves a distance of 2 m each second. b) Each particle in the Slinky moves a vertical distance of 0.04 m during each period of the wave. c) Each particle in the Slinky moves a horizontal distance of 0.04 m during each period of the wave. d) Each particle in the Slinky moves a vertical distance of 0.02 m during each period of the wave. e) Each particle in the Slinky has a wavelength of 0.04 m.
23. 16.2.4. A sound wave is being emitted from a speaker with a frequency f and an amplitude A . The sound waves travel at a constant speed of 343 m/s in air. Which one of the following actions would reduce the wavelength of the sound waves to one half of their initial value? a) increase the frequency to 2 f b) increase the amplitude to 2 A c) decrease the frequency to f /4 d) decrease the frequency to f /2 e) decrease the amplitude to A /2
24. Problem: Sound travels at approximately 340 m/s, and light travels at 3.0 x 10 8 m/s. Approximately how far away is a lightning strike if the sound off the thunder arrives at a location 2.0 seconds after the lightning is seen? (Hint: assume light moves instantaneously)
25. Problem: The frequency of an oboe's A is 440 Hz. What is the period of this note? Assume a speed of sound in air of 340 m/s.
26. Problem: The frequency of an oboe's A is 440 Hz. What is the wavelength? Assume a speed of sound in air of 340 m/s.
27. Chapter 16: Waves & Sounds Section 3: The Speed of a Wave on a String (AP?)
28. Speed of a Wave in a String The speed at which the wave moves to the right depends on how quickly one particle of the string is accelerated upward in response to the net pulling force. tension linear density
29. Example 2 Waves Traveling on Guitar Strings Transverse waves travel on each string of an electric guitar after the string is plucked. The length of each string between its two fixed ends is 0.628 m, and the mass is 0.208 g for the highest pitched E string and 3.32 g for the lowest pitched E string. Each string is under a tension of 226 N. Find the speeds of the waves on the two strings. High E Low E
30. Conceptual Example 3 Wave Speed Versus Particle Speed Is the speed of a transverse wave on a string the same as the speed at which a particle on the string moves?
31. 16.3.1. The tension of a guitar string in increased by a factor of 4. How does the speed of a wave on the string increase, if at all? a) The speed of a wave is reduced to one-fourth the value it had before the increase in tension. b) The speed of a wave is reduced to one-half the value it had before the increase in tension. c) The speed of a wave remains the same as before the increase in tension. d) The speed of a wave is increased to two times the value it had before the increase in tension. e) The speed of a wave is increased to four times the value it had before the increase in tension.
32. 16.3.2. Two identical strings each have one end attached to a wall. The other ends are each attached to a separate spool that allows the tension of each string to be changed independently. Consider each of the waves shown. Which one of the following statements is true if the frequency and amplitude of the waves is the same? a) The tension in the string on which wave A is traveling is four times that in the string on which wave D is traveling. b) The tension in the string on which wave B is traveling is four times that in the string on which wave D is traveling. c) The tension in the string on which wave B is traveling is four times that in the string on which wave A is traveling. d) The tension in the string on which wave D is traveling is four times that in the string on which wave A is traveling. e) The tension in the string on which wave C is traveling is four times that in the string on which wave B is traveling.
33. 16.3.3. A climbing rope is hanging from the ceiling in a gymnasium. A student grabs the end of the rope and begins moving it back and forth with a constant amplitude and frequency. A transverse wave moves up the rope. Which of the following statements describing the speed of the wave is true? a) The speed of the wave decreases as it moves upward. b) The speed of the wave increases as it moves upward. c) The speed of the wave is constant as it moves upward. d) The speed of the wave does not depend on the mass of the rope. e) The speed of the wave depends on its amplitude.
34. 16.3.4. When a wire is stretched by a force F , the speed of a traveling wave is v . What is the speed of the wave on the wire when the force is doubled to 3 F ? a) v b) 3 v c) 9 v d) e)
35. Chapter 16: Waves & Sounds Section 4: The Mathematical Description of a Wave (AP?)
36. What is the displacement y at time t of a particle located at x ?
37. 16.4.1. A radio station broadcasts its radio signal at a frequency of 101.5 MHz. The signals travel radially outward from a tower at the speed of light. Which one of the following equations represents this wave if t is expressed in seconds and x is expressed in meters? a) y = 150 sin[(6.377 10 8 ) t (2.123) x ] b) y = 150 sin[(637.7) t (2.961) x ] c) y = 150 sin[(6.283 10 6 ) t (2.961 10 3 ) x ] d) y = 150 sin[(101.5 10 6 ) t (2.961) x ] e) y = 150 sin[(101.5 10 6 ) t (2.123) x ]
38. 16.4.2. The equation for a certain wave is y = 4.0 sin [2 (2.5 t + 0.14 x )] where y and x are measured in meters and t is measured in seconds. What is the magnitude and direction of the velocity of this wave? a) 1.8 m/s in the + x direction b) 1.8 m/s in the x direction c) 18 m/s in the x direction d) 7.2 m/s in the + x direction e) 0.35 m/s in the x direction
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40. 16.4.4. Which one of the following correctly describes a wave described by y = 2.0 sin(3.0 x 2.0 t ) where y and x are measured in meters and t is measured in seconds? a) The wave is traveling in the + x direction with a frequency 6 Hz and a wavelength 3 m. b) The wave is traveling in the x direction with a frequency 4 Hz and a wavelength / 3 m. c) The wave is traveling in the + x direction with a frequency Hz and a wavelength 3 m. d) The wave is traveling in the x direction with a frequency 4 Hz and a wavelength m. e) The wave is traveling in the + x direction with a frequency 6 Hz and a wavelength / 3 m.
43. Sound waves in 2D Individual air molecules are not carried along with the wave.
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47. 16.5.1. A particle of dust is floating in the air approximately one half meter in front of a speaker. The speaker is then turned on produces a constant pure tone as shown. The sound waves produced by the speaker travel horizontally. Which one of the following statements correctly describes the subsequent motion of the dust particle, if any? a) The particle of dust will oscillate left and right with a frequency of 226 Hz. b) The particle of dust will oscillate up and down with a frequency of 226 Hz. c) The particle of dust will be accelerated toward the right and continue moving in that direction. d) The particle of dust will move toward the right at constant velocity. e) The dust particle will remain motionless as it cannot be affected by sound waves.
48. 16.5.2. While constructing a rail line in the 1800s, spikes were driven to attach the rails to cross ties with a sledge hammer. Consider the sound that is generated each time the hammer hits the spike. How does the frequency of the sound change, if at al, as the spike is driven into the tie? a) The frequency of the sound does not change as the spike is driven. b) The frequency of the sound decreases as the spike is driven. c) The frequency of the sound increases as the spike is driven.
50. Speed of Sound Sound travels through gases, liquids, and solids at considerably different speeds.
51. Speed of Sound In a gas, it is only when molecules collide that the condensations and rarefactions of a sound wave can move from place to place. Ideal Gas
52. Conceptual Example 5 Lightning, Thunder, and a General Rule There is a general rule for estimating how far away a thunderstorm is. After you see a flash of lighting, count off the seconds until the thunder is heard. Divide the number of seconds by five. The result gives the approximate distance (in miles) to the thunderstorm. Why does this rule work?
54. 16.6.1. In a classroom demonstration, a physics professor breathes in a small amount of helium and begins to talk. The result is that the professor’s normally low, baritone voice sounds quite high pitched. Which one of the following statements best describes this phenomena? a) The presence of helium changes the speed of sound in the air in the room, causing all sounds to have higher frequencies. b) The professor played a trick on the class by tightening his vocal cords to produces higher frequencies in his throat and mouth than normal. The helium was only a distraction and had nothing to do with it. c) The helium significantly alters the vocal chords causing the wavelength of the sounds generated to decrease and thus the frequencies increase. d) The wavelength of the sound generated in the professor’s throat and mouth is only changed slightly, but since the speed of sound in helium is approximately 2.5 times larger than in air, therefore the frequencies generated are about 2.5 times higher.
55. 16.6.2. The graph shows measured data for the speed of sound in water and the density of the water versus temperature. From the graph and your knowledge of the speed of sound in liquids, what can we infer about the bulk modulus of water in the temperature range from 0 to 100 C? a) The bulk modulus of water increases linearly with temperature. b) The bulk modulus of water decreases non-linearly with temperature. c) The bulk modulus of water is constant with increasing temperature. d) The bulk modulus of water increases non-linearly with increasing temperature. e) The bulk modulus of water increases with increasing temperature until it peaks around 60 C after which it slowly decreases.
56. 16.6.3. Ethanol has a density of 659 kg/m 3 . If the speed of sound in ethanol is 1162 m/s, what is its adiabatic bulk modulus? a) 1.7 10 8 N/m 2 b) 2.2 10 8 N/m 2 c) 7.7 10 8 N/m 2 d) 8.9 10 8 N/m 2 e) 6.1 10 9 N/m 2
59. Example 6 Sound Intensities 12x10 -5 W of sound power passed through the surfaces labeled 1 and 2. The areas of these surfaces are 4.0m 2 and 12m 2 . Determine the sound intensity at each surface.
60. Perception of Intensity For a 1000 Hz tone, the smallest sound intensity that the human ear can detect is about 1x10 -12 W/m 2 . This intensity is called the threshold of hearing . On the other extreme, continuous exposure to intensities greater than 1W/m 2 can be painful. If the source emits sound uniformly in all directions, the intensity depends on the distance from the source in a simple way.
62. Conceptual Example 8 Reflected Sound and Sound Intensity Suppose the person singing in the shower produces a sound power P. Sound reflects from the surrounding shower stall. At a distance r in front of the person, does the equation for the intensity of sound emitted uniformly in all directions underestimate, overestimate, or give the correct sound intensity?
63. 16.7.1. Natalie is a distance d in front of a speaker emitting sound waves. She then moves to a position that is a distance 2 d in front of the speaker. By what percentage does the sound intensity decrease for Natalie between the two positions? a) 10 % b) 25 % c) 50 % d) 75% e) The sound intensity remains constant because it is not dependent on the distance.
64. 16.7.2. A bell is ringing inside of a sealed glass jar that is connected to a vacuum pump. Initially, the jar is filled with air at atmospheric pressure. What does one hear as the air is slowly removed from the jar by the pump? a) The sound intensity gradually increases. b) The sound intensity gradually decreases. c) The sound intensity of the bell does not change. d) The frequency of the sound gradually increases. e) The frequency of the sound gradually decreases.
66. The Decibel Scale The decibel (dB) is a measurement unit used when comparing two sound intensities. Because of the way in which the human hearing mechanism responds to intensity, it is appropriate to use a logarithmic scale called the intensity level: Note that log(1)=0, so when the intensity of the sound is equal to the threshold of hearing, the intensity level is zero.
68. Example 9 Comparing Sound Intensities Audio system 1 produces a sound intensity level of 90.0 dB, and system 2 produces an intensity level of 93.0 dB. Determine the ratio of intensities.
69. 16.8.1. A sound level meter is used measure the sound intensity level. A sound level meter is placed an equal distance in front of two speakers, one to the left and one to the right. A signal of constant frequency may be sent to each of the speakers independently or at the same time. When either the left speaker is turned on or the right speaker is turned on, the sound level meter reads 90.0 dB. What will the sound level meter read when both speakers are turned on at the same time? a) 90.0 dB b) 93.0 dB c) 96.0 dB d) 100.0 dB e) 180.0 dB
70. 16.8.2. A sound level meter is used measure the sound intensity level. A sound level meter is placed an equal distance in front of two speakers, one to the left and one to the right. A signal of constant frequency, but differing amplitude, is sent to each speaker independently. When the left speaker is turned on the sound level meter reads 85 dB. When the right speaker is turned on the sound level meter reads 65 dB. What will the sound level meter read when both speakers are turned on at the same time? a) about 85 dB b) about 65 dB c) about 150 dB d) about 75 dB e) about 113 dB
71. 16.8.3. Software is used to amplify a digital sound file on a computer by 20 dB. By what factor has the intensity of the sound been increased as compared to the original sound file? a) 2 b) 5 c) 10 d) 20 e) 100
74. The Doppler Effect Stationary source Subsonic source Source breaking sound barrier Supersonic source Animations courtesy of Dr. Dan Russell, Kettering University
76. Doppler Effect source moving toward a stationary observer source moving away from a stationary observer
77. Example 10 The Sound of a Passing Train A high-speed train is traveling at a speed of 44.7 m/s when the engineer sounds the 415-Hz warning horn. The speed of sound is 343 m/s. What are the frequency and wavelength of the sound, as perceived by a person standing at the crossing, when the train is (a) approaching and (b) leaving the crossing? approaching leaving
79. Doppler Effect – Moving Observer Observer moving towards stationary source Observer moving away from stationary source
80. General Doppler Equation Numerator: plus sign applies when observer moves towards the source Denominator: minus sign applies when source moves towards the observer
81. 16.9.1. Two stationary observers, Keisha and Trina, are listening to the sound from a moving source. The sound from the source has a constant frequency f S and constant amplitude. As the source moves, Trina hears two different frequencies f 1 and f 2 , where f 1 > f S and f 2 < f S . Keisha, who is not moving with the source, only hears one frequency, f . Which one of the following statements best explains this situation?. a) The source is moving very slowly relative to Keisha, but fast relative to Trina. b) The source is moving along a parabolic path and Keisha is at the origin of the parabola. Trina is inside the parabola. c) Keisha is standing at a location where the wind is blowing in such a way as to remove the Doppler effect, while Trina is standing in a location where there is no wind. d) The source is moving along a circle and Keisha is at the center of the circle. Trina is outside the circle. e) The source is moving along an ellipse and Keisha is at one of the two foci of the ellipse. Trina is outside the ellipse.
82. 16.9.2. A child is swinging back and forth with a constant period and amplitude. Somewhere in front of the child, a stationary horn is emitting a constant tone of frequency f S . Five points are labeled in the drawing to indicate positions along the arc as the child swings. At which position(s) will the child hear the lowest frequency for the sound from the whistle? a) at B when moving toward A b) at B when moving toward C c) at C when moving toward B d) at C when moving toward D e) at both A and D
83. 16.9.3. Hydrogen atoms in a distant galaxy are observed to emit light that is shifted to lower frequencies with respect to hydrogen atoms here on Earth. Astronomers use this information to determine the relative velocity of the galaxy with respect to the Earth by observing how light emitted by atoms is Doppler shifted. For the hydrogen atoms mentioned, how are the wavelengths of light affected by the relative motion, if at all? a) The wavelengths would be unchanged, only the frequencies are shifted. b) The wavelengths of light would be longer than those observed on Earth. c) The wavelengths of light would be shorter than those observed on Earth.
84. Chapter 16: Waves & Sounds Section 10: Applications of Sound in Medicine (Not AP)
85. Applications of Sound in Medicine By scanning ultrasonic waves across the body and detecting the echoes from various locations, it is possible to obtain an image.
86. Applications of Sound in Medicine Ultrasonic sound waves cause the tip of the probe to vibrate at 23 kHz and shatter sections of the tumor that it touches.
87. Applications of Sound in Medicine When the sound is reflected from the red blood cells, its frequency is changed in a kind of Doppler effect because the cells are moving.
88. Chapter 16: Waves & Sound Section 11: The Sensitivity of the Human Ear (Not AP)
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