{[ promptMessage ]}

Bookmark it

{[ promptMessage ]}

Ch15HW - (an a 318 Chapter 15 Vibrations and Waves...

Info icon This preview shows pages 1–5. Sign up to view the full content.

View Full Document Right Arrow Icon
Image of page 1

Info icon This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document Right Arrow Icon
Image of page 2
Image of page 3

Info icon This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document Right Arrow Icon
Image of page 4
Image of page 5
This is the end of the preview. Sign up to access the rest of the document.

Unformatted text preview: (an a) 318 Chapter 15 Vibrations and Waves amplitude: The maximum distance from the equilibrium pow sition that occurs in periodic motion. antinode: One of the positions in a standing wave or interfer- ence pattern where there is maximal movement; that is, the ain- plitude is a maximum. crest: The peak ofa wave disturbance. cycle: One complete repetition of a periodic motion. It may start anyplace in the motion. diffraction: The spreading of waves passing through an open- ing or around a barrier. displacement: In wave {or oscillatory) motion, the distance of the disturbance (or object} from its equilibrium position. equilibrium position: A position where the net force is zero. frequency: The number of times a periodic motion repeats in a unit of time. It is equal to the inverse of the period fundamental frequency: The lowest resonant frequency for an oscillating system. harmonic: A frequency that is a whole-number multiple of the fundamental frequency. in phase: Two or more waves with the same wavelength and frequency that have their crests lined up. interference: The superposition of waves. longitudinal wave: A wave in which the vibrations of the medium are parallel to the direction the wave is mming. node: One of the positions in a standing wave or interference pattern where there is no movement: that is, the amplitude is zero. l. Ifthe net force on a mass oscillating at the end ofa vertical spring is zero at the equilibrium point, why doesn’t the mass stop there? 2. If the restoring force on a pendulum is zero when it is ver— tical, why doesn‘t it quit swinging at this point? @A mass is oscillating up and down on a vertical spring. When the mass is above the equilibrium point and moving down, what direction is the net force on the mass? When the mass is above the equilibrium point and moving up, what direction is the net force on the mass? 4. A mass is oscillating up and down on a vertical spring. When the mass is below the equilibrium point and moving down, what direction is its acceleration? Is the mass speed- ing up or slowing down? mass is oscillating up and down on a vertical spring. if the mass is increased, will the period of oscillation increase, def KEY TERMS CONCEPTUAL QUESTIONS oscillation: A vibration about an equilibrium position or shape. period: The shortest length of time it takes a periodic motion to repeat. It is equal to the inverse of the frequency. periodic wave: A wave in which all the pulses have the same size and shape. The wave pattern repeats itself over a distance of one wavelength and over a time of one period. resonance: A large increase in the amplitude of a vibratiop, when :1 force is applied at a natural frequency of the medium or object. spring constant: The amount of force required to stretch a spring by one unit of length. Measured in newtons per meter, standing wave: The interference pattern produced by two waves of equal amplitude and frequency trawling in opposite directions. The pattern is characterized by alternating nodal and antinodal regions. superposition: The combinng of two or more waves at a loca“ tion in space. transverse wave: A wave in which the vibrations of the medium are perpendicular to the direction the wave is moving. trough: A valley of a wave disturbance. vibration: An oscillation about an equilibrium position or shape. wave: The movement of energy from one place to another without any accompanying matter. wavelength: The shortest repetition length for a periodic ware. For example, it is the distance from (rest to crest or [rough to trough. crease, or stay the same? Will the frequency increase, de- crease, or stay the same? 6. You have a grandfather clock (with a pendulum) that'keeps perfect time on Earth. if you were to transport this clock to the Moon, would its period ot‘Oscillation increase, decrease, or stay the same? would its frequency increase, decrease, 01‘ stay the same? Explain. 7. You hang a likilogram block from a spring and find that the spring stretches 15 centimeters. What mass of block would you need to stretch the spring by 45 centimeters? 8. Which spring would you expect to have the greater spring constant, the one in the suspension of your Chevy or the one in the mechanism of your watch? Why? 9. Assume that you pull the mass on the spring 1 centimeter from the equilibrium position, let go, and measure the [36‘ I‘iod of the oscillation. Would you expect the period to be m.mr» are; .4 ,u ._ "not” i I0. I2. [3. *I4. l5. l8. i larger, the same, or smaller if you pulled the mass 2 cen— timeters from the equilibrium position? Why? The amplitudes of real pendula decrease because of fric— tional forces. How does the period of a real pendulum change as it dies down? tat is the period of the hand on a clock that measures the seconds? What is its frequency? What is the period of the hand on a clock that measures the minutes? What is its frequency? ' Suppose your grandfather clock runs too fast. If the mass on the pendulum can be moved up or down, which way would you move it to adjust the clock? Explain your reasoning. How does the natural frequency of a swing change when you move from sitting down to standing up? You find that the exhaust system on your 1979 Chrysler Cordoba tends to rattle loudly when the tachometer, which measures the engine's frequency, reads ‘20th rpm. it is relatively quiet at frequencies above or below this. Use the concept of resonance to explain this. Why do soldiers “break step” before crossing a suspension bridge? You hold one end of a spring in your hand and hang a block from the other end. After lifting the block up slightly and releasing it, you find that it oscillates up and down at a frequency of 2 hertz. At which of the following frequencies could youjiggle your hand tip and down and produce resonance: 5 hertz, 4 hertz, l.5 hertz, l hertz, or 0.5 hertz? You stand to the side of the low point ofa child’s swing and always push the child in the same direction. Which of the following multiples of the fundamental frequency will not produce resonance: %, 12, l, or 2? When you yell at your friend, are the air molecules that strike his ear the same ones that were in your lungs? Explain. What is being transported along a clothesline when a wave moves from one end to the other? 21. 22. 23. 24. 25. 26. 27. 28. '\ Conceptual Questions 3 i 9 ‘- ._ Sonar devices use underwater sound to explore the ocean floor. Would you expect sonar to he a longitudinal or a transverse wave? Explain. You fasten one end ofa long spring to the base ofa wall and stretch it out along the floor, holding the other end in your hand. Describe how you would generate a transverse pulse on the spring. Describe how you would generate a longitu- dinal pulse on the spring. Is it possible for a shout to overtake a whisper? Explain. You stretch a long spring between a doorknob and your hand. You generate a small transverse pulse on the spring traveling toward the doorknob. How could you generate a second pulse that would overtake the first pulse? Which of the following properties affect the speed of waves along a rope: amplitude of the pulse, shape of the pulse, tension in the rope, and/or the mass per unit length of the rope? Why? You stretch a long spring between a doorknob and your hand. You jerk your hand up and down to send a pulse down the spring. Ifyou want to generate a slower-traveling pulse, which of the following woulcl you do? Move your hand up and down the same distance as before but do it more slowly; move your hand up and down a smaller dis— tan ce at the same speed as before; or move slightly closer to the doorknob to decrease the tension in the spring. You fasten one end of a long spring to the base of a wall and stretch it out along the floor, holding the other end in your hand. You send a pulse of amplitude 5 centimeters down the right side of the spring, and a moment later you send a second identical pulse on the same side. The first pulse reflects from the fixed boundary and returns along the spring toward you. When the reflected pulse meets the secw 0nd pulse, will the resulting amplitude be less than, equal to, or greater than 5 centimeters? Explain your reasoning. imagine that the string in Figure 1544 is tied to the pole with a loose loop such that the end is free to move up and 320 Chapter 15 Vibrations and Waves down. A pulse of amplitude 10 centimeters is sent down the top of the string, and a moment later a second identical pulse is sent, also on the top. The first pulse reflects from the free boundary and returns along the string. When the rellected pulse meets the second pulse, will the resulting amplitude be less than, equal to, or greater thart lU centir meters? Explain your reasoning. 29. The pulse in the figure is traveling on a stringr to the right toward a fixed end. Draw the shape of the pulse after it reflects from the boundary. 30. A pulse in the shape of a crest is sent from left to right along a stretched rope. A trough travels in the opposite direction so that the pulses meet in the middle of the rope. Would you expect to observe a crest or a trough arrive at the righb ; I hand end of the rope? Explain. . .Il‘shapcs a and b in the figure correspond to idealized wave l I pulses on a rope, what shape is produced when they conr pletely overlap? (a) ’__‘ 32. Repeat Question 31 for shapes :1 and c. 33. Which of the following properties are meaningful for peri- odic waves but not for single pulses: frequency, wavelength, speed, amplitude? 34. In the following list of properties of periodic waves, which one is independent Of the others: frequency, wavelength, speed, amplitude? 35. Two waves have the same speed but one has twice the free quency of the other. Which one has the longer wavelength? Explain. 36. If the frequency of a periodic wave is cut in half while the speed remains the same, what happens to the wavelength? 37. lfthe speed ofa periodic wave doubles while the period re- mains the Same, what happens to the wavelength? 38. What happens to the wavelength ofa periodic wave if both the speed of the wave and the frequency are cttt in half? 39. 40. 4|. 42. 43. 44. 45. Cuustesv cl Philadelphia International Airport Travelers are spaced 10 feet apart on a moving sidewalk in an airport. They are all walking at exactly 3 mph relative to the sidewalk. \Nhen the moving sidewalk ends, they con- tinue to walk at 3 mph. An obseiver standing still next to the movingr sidewalk notes that the travelers are passing at a frequency of l hertz. A second obsewer stands just be- yond the end of the moving sidewalk and notes the fre- quency at which the travelers pass. Would this frequency be greater than, equal to, or less than i hertz? is the spacing between the travelers after leaving the moving sidewalk greater than, equal to, or less than 10 feet? Explain. A waterproof electric buzzer has a membrane that vibrates at a constant frequency of 440 hertz. The buzzer is placed in a bucket of water. Knowing that the speed of sound is much greater in water than in air, will the frequency of the sound heard in th * air be greater than, equal to, or less than 440 hertz? \Nill the wavelength of the sound in air be greater than, equal to, or less than what it was in the water? Explain (Hint: Review Question 39 and think of the travel- ers as the wave crests.) Draw a diagram to represent the standing-wave pattern for the third harmonic of a rope fixed at both ends. How many antinodes are there when a rope fixed at both ends vibrates in its third harmonic? Draw a diagram to represent the standing-wave pattern for the fourth harmonic ofa rope fixed at both ends. How many nodes are there when a rope fixed at both ends vibrates in its fourth harmonic? How much higher is the frequency of the fifth harmonic on a rope than the fundamental frequency? How much higher is the frequency of the sixth harmonic on a rope than that of the second? Standing waves can be established on a rope that is fixed on one end but free to slide up and down a pole on the other. The fixed end remains a node, while the free end must be an antiuode. Draw diagrams to represent the standing- wave patterns for the two lowest frequencies. How does the fundamental wavelength of standing waves on a string with one end fixed and the other free compare to the fundamental wavelength if the same sn‘ing‘is held with both ends fixed? How does the wavelength of the fourth harmonic on a rope with both ends fixed compare with the length of the rope? How does the wavelength of the fourth harmonic on a rope with both ends fixed compare with that of the second harmonic? A longitudinal standing wave can be established in a long aluminum rod by stroking it with rosin on your fingers. If the rod is held tightly at its midpoint, what is the wave- length of the fundamental standing wave? Assume that there are antinodes at each end of the rod and a node where the rod is held. What is the wavelength of the fundamental standing wave for the rod in Question 51 ifit is held midway between the center and one end? Will the resulting pitch be higher or lower than when the rod was held at its midpoint? Explain. Two point sources produce waves of the same wavelength and are in phase. At a point midway between the sources, Would you expect to find a node or an antinode? Explain. Two point sources produce waves of the same wavelength and are completely out of phase (that is, one produces a crest at the same time as the other produces a trough}. *55. *56. 57. Cnurtesy at Central Scientific Company 58. Exercises 3 2 I At a point midway between the sources, would you expect to find a node or an antinode? Why? What happens to the spacing of the antinodal lines in an interference pattern when the two sources are moved far~ ther apart? Explain. As you increase the frequency of the sources, what hap- pens to the spacing of the nodal lilies in an interference pattern produced by two sources? Explain. An interference pattern is produced in a ripple tank. As the two sources are brought closer together, does the sep- aration of the locations of maximum amplitude along the far edge of the tank decrease, increase, or remain the same? Why? As the frequency of the two sources forming an inter- ference pattern in a ripple tank increases, does the sepa~ ration of the locations of minimum amplitude along the far edge of the tank increase, decrease, or remain the same? Why? EXERCISES If a mass on a spring takes 6 s to complete two cycles, what is its period? If a mass on a spring has a frequency of 4 Hz, what is its period? ®A Foucault pendulum with a length of 9 m has a period of 6 5. What is its frequency? 4- A mass on a spring bobs up and down over a distance of 30 cm from the top to the bottom ofits path twice each sec- ond. What are its period and amplitude? 5- A spring hanging from the ceiling has an unstretched length of 80 cm. A mass is then suspended at rest from the spring, causing its length to increase to 89 cm. The mass is pulled down an additional 3 cm and released. What is the amplitude of the resulting oscillation? 6. '\. IO. / A mass oscillates up and down on a vertical spring with an amplitude of 4 cm and a period of 2 5. What total distance does the mass travel in 10 seconds? ‘Nhat is the period of a 0.4—kg mass suspended from a spring with a spring constant of 40 N/rn? A boy with a mass of 50 kg is hanging from a spring with a spring constant of 200 N/m. With what frequency does the boy bounce up and down? oi By what factor would you have to increase the spring con- stant to double the frequency for a mass on a spring? By what factor would you have to increase the mass to triple the period for a mass on a spring? A pendulum has a length offi m. What is its period? l/R 322 I2. *I3. *l4. I5. “3. I9. Chapter 15 Vibrations and Waves 8 distance, cm A girl with a mass of 40 kg is swinging-from a rope with a length of 2.5 m. What is the frequency of her swinging? The highly idealized wave pulses shown in the figure at a Lime equal to zero have the same amplitudes and travel at 1 cm/s. Draw the shape of the rope at 2, 4, 5, and 8 5. Work Exercise 13 but change the rectangular pulse from a crest to a trough. A train, consisting of identical lO-m boxcar-s, passes you such that 2:3 boxcars pass you each minute. Find the speed of the train. . You observe that 25 crests of a water wave pass you each minute. If the wavelength is 10 In, what is the speed of the wave? A periodic wave on a string has a wavelength of 25 cm and a frequency of 3 Hz. What is the speed of the wave? If the breakers at a beach are separated by 5 m and hit shore with a frequency of 0.3 Hz, at what speed are they traveling? What is the distance between adjacent crests of ocean waves that have a frequency 0f().‘2 Hz if the waves have a speed of 3 Iii/s? 20. 2|. /2. .A rope is tied between two posts separated by 3 in. What *24. *25. *26. 10 12 16 Sound waves in iron have a speed of about 5] 00 ni/s. if the waves have a frequency of‘iOO Hz, what is their wavelength? For sound waves, which travel at 343 m/s in air at room temperature, what frequency corresponds to awavelength of l m? What is the period of waves on a rope if their wavelength is 0.8 In and their speed is 2 m/s? possible wavelengths will produce standing waves on the rope? A 3-m-long rope is tied to a very thin string so that one end is essentially free. “That possible wavelengths will pro— duce standing waves on this rope? ‘Nhat is the fundamental frequency on 21 6—111 rope that is tied at both ends if the speed of the waves is 18 m/s? Tweety Bird hops up and down at a frequency of0.5 Hz on a power line at the midpoint between the poles, which are separated by 20 In. Assuming Tweety is exciting the fun- damental standing wave, find the speed of transverse waves on the power line. (Hint: What is the wavelength for this standing wave?) ”"iiilnfoTrac‘E College Edition For additional readings, explore InfoTrac College Edition, your online library. Go to http1//V\ww.infotrac—coliege.com/wadsworth and use the passcode that came on the card with your book. Try these search terms: atomic clock, Christiaan Huygens,john Harrison and chronometerJohn Harrison and clock, pendulum clock, seismic waves, standing waves, ‘ Tacoma Narrows Bridge. ...
View Full Document

{[ snackBarMessage ]}

What students are saying

  • Left Quote Icon

    As a current student on this bumpy collegiate pathway, I stumbled upon Course Hero, where I can find study resources for nearly all my courses, get online help from tutors 24/7, and even share my old projects, papers, and lecture notes with other students.

    Student Picture

    Kiran Temple University Fox School of Business ‘17, Course Hero Intern

  • Left Quote Icon

    I cannot even describe how much Course Hero helped me this summer. It’s truly become something I can always rely on and help me. In the end, I was not only able to survive summer classes, but I was able to thrive thanks to Course Hero.

    Student Picture

    Dana University of Pennsylvania ‘17, Course Hero Intern

  • Left Quote Icon

    The ability to access any university’s resources through Course Hero proved invaluable in my case. I was behind on Tulane coursework and actually used UCLA’s materials to help me move forward and get everything together on time.

    Student Picture

    Jill Tulane University ‘16, Course Hero Intern