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physics
college physics a strategic approach 2nd

College Physics Essentials Electricity And Magnetism Optics Modern Physics Volume Two 8th Edition Jerry D. Wilson, Anthony J. Buffa, Bo Lou - Solutions

6. The Richter scale, used to measure the intensity level of earthquakes, is a logarithmic scale, as is the decibel scale. Why are such logarithmic scales used?
5. Where is the intensity greater and by what factor: (1) at a distance R from a small sound source of power P, or(2) at a distance 2R from a small sound source of power 2P? Explain.
4. What role, if any, do you think humidity should play on the speed of sound in air?
3. Explain why the speed of sound in helium is a lot faster than in air. [Hint: Check out the molecular masses.]
2. As a sound wave travels from warm air into cold air, explain how its frequency, wavelength, and speed change.
1. The speed of sound in air does not depend on frequency.Explain how this enables concert goers in all seats to hear the same music in the right sequence/combination.
15. The human ear can hear tones best at about what frequency?(a) 1000 Hz, (b) 4000 Hz, (c) 6000 Hz,(d) all frequencies.
14. Given open-open and open-closed pipes of the same length, which would have the lowest natural frequency:(a) the open-open pipe, (b) the open-closed pipe, or(c) they both would have the same lowest frequency?
13. Police radar equipment measure speeds based on(a) refraction, (b) the Doppler effect, (c) diffraction,(d) sonic boom.
12. Beats are the direct result of (a) the principle of superposition,(b) refraction, (c) diffraction, (d) the Doppler effect.
11. Constructive and destructive interference of sound waves is based on (a) the speed of sound, (b) diffraction,(c) phase difference, (d) the principle of superposition.
10. A sound with an intensity level of 30 dB is how many times more intense than the threshold of hearing:(a) 10, (b) 100, (c) 1000, or (d) 3000?
9. The intensity of a sound wave is directly proportional to the (a) amplitude, (b) frequency, (c) square of the amplitude, (d) square of the frequency.
8. If the intensity level of a sound at 20 dB is increased to 40 dB, the intensity would increase by a factor of(a) 10, (b) 20, (c) 40, (d) 100.
7. The decibel scale is referenced to a standard intensity of (a) 1.0 W/m2, (b) 10−12 W/m2, (c) normal conversation,(d) the threshold of pain.
6. If the air temperature increases, would the sound intensity from a constant-output point source(a) increase, (b) decrease, or (c) remain unchanged?
5. The speed of sound in water is about 4 times that in air.A single-frequency sound source in air is fo. When its sound goes from air into water, the frequency of the sound in the water will be (a) 4fo, (b) fo/4, (c) fo.
4. The speed of sound in air (a) is about 1/3 km/s, (b) is about 1/5 mi/s, (c) depends on temperature, (d) all of the preceding.
3. The speed of sound is generally greatest in (a) solids,(b) liquids, (c) gases, (d) a vacuum.
2. A sound wave in air (a) is longitudinal, (b) is transverse,(c) has longitudinal and transverse components,(d) travels faster than a sound wave through a liquid.
1. A sound wave with a frequency of 15 Hz is in what region of the sound spectrum: (a) audible, (b) infrasonic,(c) ultrasonic, or (d) supersonic?
58. ••• A uniform string with a length of 1.80 m is tied tightly at both ends under a tension of 100 N. When it vibrates in its third harmonic (draw a sketch?), the sound given off has a frequency of 75.0 Hz. What is the mass of the string?
57. IE •• A violin string is tuned to its fundamental, or first harmonic, frequency. (a) If a violinist wants a higher frequency by changing only its length, should the string be (1) lengthened, (2) kept the same, or(3) shortened? Why? (b) If the string is tuned to 520 Hz and the violinist puts
56. •• You want to set up two standing string waves using a length of uniform piano wire that is 3.0 m long with a mass of 0.150 kg. You cut it into two segments, one with a length of 1.0 m and the other 2.0 m, and then place each under tension. What should be the ratio of tensions (expressed
55. IE •• String A has twice the tension but half the linear mass density of string B, and both have the same length. (a) The frequency of the first harmonic on string A is (1) four times, (2) twice, (3) half, (4) 1/4 times that of string B. Explain. (b) If the length of the strings is 2.5 m
54. •• A physics professor buys 100 m of string with a total mass of 0.150 kg. This string is used to set up a standing wave lecture demonstration between two posts 3.0 m apart. If the desired second harmonic frequency is 35 Hz, what should be the string tension?
53. •• Two waves of equal amplitude and frequency of 250 Hz travel in opposite directions at a speed of 150 m/s in a string. If the string is 0.90 m long, for which harmonic mode is the standing wave set up in the string?
52. •• Will a standing wave be formed in a 4.0-m length of stretched string that has a wave speed of 12 m/s if it is driven at a frequency of (a) 15 Hz or (b) 20 Hz?
51. •• On a violin, a correctly tuned “A” string has a frequency of 440 Hz. If an “A” string produces sound at 450 Hz under a tension of 500 N, what should the tension be to produce the correct frequency, assuming the string length remains unchanged?
50. IE •• A piece of thin steel cable is under tension.(a) If the tension doubles, the wave speed on the cable(1) doubles, (2) halves, (3) increases by 2 , (4) decreases by 2 . Why? (b) If the linear mass density of the cable is 0.125 kg/m and it is under a tension of 9.00 N, what is the wave
49. • If the wavelength of the third harmonic on a string is 5.0 m, what is the string length?
48. • A standing wave is formed in a stretched string that is 3.0 m long. What are the wavelengths of (a) the first harmonic and (b) the second harmonic?
47. • If the frequency of the fifth harmonic of a vibrating string is 425 Hz, what is the frequency of the second harmonic?
46. • The fundamental frequency of a stretched string is 150 Hz. What are the frequencies of (a) the second harmonic and (b) the third harmonic?
45. • If the frequency of the third harmonic on a tight string is 600 Hz, what is the frequency of the first harmonic?
43. •• A submarine’s sonar generator produces ultrasonic sound waves at 2.50 MHz. The wavelength of the waves in seawater is 4.80 × 10−4 m. When the generator is directed downward, an echo reflected from the ocean floor is received 10.0 s later. How deep is the ocean at that point,
42. • Light waves travel in a vacuum at a speed of 3.00 × 108 m/s. The frequency of blue light is about 6.0 × 1014 Hz. What is the approximate wavelength of this blue light?
41. • Bats can determine the location of prey using echolocation(measuring the travel time for a sound echo to return). If it takes 15 ms for a bat to receive an ultrasonic(i.e., above the frequency of human hearing) sound wave reflected off a mosquito, how far is the mosquito from the bat? Take
40. • A student reading his physics book on a dock notices that the distance between two successive incoming wave crests is 0.75 m, and the difference in their times of arrival is 1.6 s. What is the speed of the water waves?
39. • A wave on a very long rope takes 2.0 s to travel 10 m of the rope. If the wavelength of the wave is 2.5 m, what is the frequency of oscillation of any piece of the rope?
38. • A sound wave travels at 340 m/s in air. If this wave has a frequency of 1000 Hz, what is its wavelength?
37. ••• The velocity of a vertically oscillating 5.00-kg mass on a spring is given by v = (−0.600 m/s)sin(6t) (a) Determine an expression for its location, y, as a function of time.(b) Where does the motion start and in what direction does the object move initially and with what speed?(c)
36. ••• A grandfather clock behaves like a simple pendulum 75 cm long. The clock is accidentally broken, and when it is repaired, the length of the pendulum is shortened by 2.0 mm. (a) Will the repaired clock gain or lose time? (b) By how much will the time on the repaired clock differ from
35. •• Assume that the motion of a 0.25-kg mass oscillating on a light spring is described by the graph for System B in Figure 13.24. (a) Write the equation for the displacement of the mass as a function of time.(b) What is the spring constant of the spring?
34. •• Assume that the motion of an object oscillating on a light spring is described by the graph for System A in Figure 13.24. (a) Write the equation of motion in terms of a sine or cosine function. (b) If the spring constant is 20 N/m, what is the mass of the object?
33. IE •• (a) If a pendulum clock were taken to the Moon, where the acceleration due to gravity is only one-sixth(take this to be exact) that on the Earth, will the period of oscillation (1) increase, (2) remain the same, or(3) decrease? Why? (b) If the period on the Earth is 2.0 s, what is the
32. •• During an earthquake, the floor of an apartment building is observed to oscillate in approximately SJM with a period of 1.95 s and an amplitude of 8.65 cm.Determine the maximum speed and acceleration of the floor during this motion.
31. •• Two masses oscillate on light springs. The second mass is half of the first and its spring constant is twice that of the first. Which system will have the greater frequency, and what is the ratio of the frequency of the second mass to that of the first mass?
30. •• What is the maximum spring potential energy of a horizontal mass-spring oscillator whose equation of motion is x = (0.350 m)sin (7t) if mass on the spring is 0.900 kg?
29. IE •• (a) If the spring constant in an oscillating massspring system is halved, the new period is (1) 2, (2) 2 ,(3) 1 2, (4) 1/2 times the old period. Explain. (b) If the initial period is 2.0 s and the spring constant is reduced to 1/3 of its initial value, what is the new period?
28. IE •• (a) If the mass in an oscillating mass-spring system is halved, the new period is (1) 2, (2) 2 , (3) 1 2, (4) 1/2 times the old period. Explain. (b) If its initial period is 3.0 s and the mass is reduced to 1/3 of its initial value, what is the new period?
27. •• The velocity of an object in a vertically oscillating mass-spring system is v = (0.750 m/s)sin(4t). Find the object’s (a) amplitude and (b) maximum acceleration.
25. •• The equation of motion of a horizontal SHM oscillator is x = (0.50 m)sin(2πft) where x is in meters and t is in seconds. If the position of the oscillator is x = 0.25 m at t = 0.25 s, what is the frequency of the oscillator?
24. • The location of an object in vertical SHM is given by y = (0.25 m)cos(314t) where y is in meters and t is in seconds. What is the location of the oscillator at(a) t = 0, (b) t = 5.0 s, and (c) t = 15 s?
23. • The location of an object in vertical SHM is y = (5.0 cm)cos(20πt). What are the system’s (a) amplitude,(b) frequency, and (c) period?
22. • The equation of motion for an oscillator in vertical SHM is y = (0.10 m)sin (100t). What are the (a) amplitude,(b) frequency, and (c) period of this motion?
21. • In each case, choose sine or cosine (with the proper sign) for the equation of motion that best describes the location (x) of a mass attached to a spring on a horizontal frictionless surface. (a) The spring is stretched and released, (b) the spring is compressed and released, and (c) the
20. • A breeze sets a suspended lamp swinging. If the period is 1.0 s, what is the distance from ceiling to lamp at the low point? Assume the lamp acts as a simple pendulum.
19. • If the frequency of a mass-spring system is 1.50 Hz and the mass on the spring is 5.00 kg, what is the spring constant?
18. • How much mass should be on the end of a spring(k = 100 N/m) so the period is 2.0 s?
17. • The simple pendulum in a tall clock is 0.75 m long.What are (a) the period and (b) the frequency of this pendulum?
16. • A 0.50-kg mass oscillates in SHM on a spring with a spring constant of 200 N/m. What are (a) the period and (b) the frequency of the oscillation?
15. ••• A 0.250-kg ball is dropped from a height of 10.0 cm onto a spring, as illustrated in ▼ Figure 13.23. If the spring has a spring constant of 60.0 N/m, (a) what distance will the spring be compressed? (Neglect energy loss during collision.) (b) On recoiling upward, how high will the
14. •• A 0.350-kg block moving vertically upward collides with a light vertical spring and compresses it 4.50 cm before coming to rest. If the spring constant is 50.0 N/m, what was the initial speed of the block?(Ignore energy losses during the collision.)
13. •• A 0.25-kg object is attached to a vertical spring of spring constant 49 N/m and the system is brought to rest at its equilibrium position. The object is then pulled down 0.10 m from equilibrium and released.What is the object’s speed as it passes equilibrium?
12. •• A 0.25-kg object is attached to a light spring of spring constant 49 N/m and gently eased to its equilibrium position where it is at rest. (a) How far does the mass stretch the string? (b) By how much does the gravitational potential energy of the spring-mass system change? (c) By how
11. •• A horizontal spring on a frictionless and level air track has a 0.150-kg object attached to it and then it is stretched 6.50 cm. Then the object is given an outward velocity of 2.20 m/s. If the spring constant is 35.2 N/m, determine how much farther the spring stretches.
10. •• A mass-spring system is in horizontal SHM. If the mass is 0.25 kg, the spring constant is 12 N/m, and the amplitude is 15 cm, (a) what is the maximum speed of the mass, and (b) where does this occur? (c) What is the speed at a half-amplitude position?
9. IE •• (a) At what position is the speed of a mass in a horizontal mass-spring system maximum: (1) x = 0,(2) x = −A, or (3) x = +A? Why? (b) If m = 0.250 kg, k = 100 N/m, and A = 0.10 m for such a system, what is the mass’s maximum speed?
8. IE •• (a) At what position is the magnitude of the force on a mass in a horizontal mass-spring system minimum:(1) x = 0, (2) x = −A, or (3) x = +A? Why? (b) If m = 0.500 kg, k = 150 N/m, and A = 0.150 m, what are the magnitude of the force on the mass and its acceleration at x = 0, 0.050
7. • An object (mass 1.0 kg) is attached to a spring with spring constant 15 N/m. If the object has a maximum speed of 50 cm/s, what is the amplitude of its oscillation?
6. • An object (mass 0.50 kg) is attached to a spring with spring constant of 10 N/m. If the object is pulled 5.0 cm from equilibrium and released, what is its maximum speed?
5. • An oscillator’s frequency changes from 0.25 Hz to 0.50 Hz. What is the period change?
4. • A particle in SHM oscillates at frequency of 40 Hz.What is its period?
3. • A 0.75-kg object on a spring completes a cycle every 0.50 s. What is the oscillation frequency?
2. • If it takes a particle in SHM 0.50 s to travel from equilibrium to maximum displacement from equilibrium, what is the period of this oscillation?
1. • A particle oscillates in SHM with an amplitude A.What is the total distance (in terms of A) the particle travels in three periods?
20. By rubbing the circular lip of a wide, thin wine glass with a moist finger, you can make the glass “sing.” (Try it.) What causes this?
19. A child’s swing (treated as a pendulum) has only one natural frequency, f1, yet it can be driven so as to maintain or increase its energy at frequencies of f1/2, f1/3, and 2f1. How is this possible?
18. If they have the same tension, mass, and length, will a thicker or a thinner guitar string sound higher in frequency?Why?
17. Is it possible to generate harmonic sound of any frequency using a violin string with a fixed tension and length? Explain.
16. If sound waves were dispersive, what would be the consequences of someone listening to an orchestra in a concert hall?
15. Dolphins and bats can determine the location of prey by emitting ultrasonic sound waves. Which wave phenomenon is involved?
14. What physical quantity(ies) is (are) cancelled when destructive interference occurs? What happens to the wave energy in such a situation? Explain.
12. What type(s) of wave(s), transverse or longitudinal, are able to propagate through (a) solids, (b) liquids, and (c) gases?
11. ▼ Figure 13.22 shows a picture of a mechanical waves traveling along a stretched coil (spring). Is it transverse or longitudinal? Explain your reasoning.
10. When a wave pulse travels along a rope, what physical quantity actually travels?
9. One simple harmonic motion is described by a sine function, y = Asin(ωt) and another is described by a cosine function, y = Acos(ωt). How do their initial positions, speeds, and accelerations compare?
8. Would the period of a pendulum in an upward-accelerating elevator be increased or decreased compared with its period in a non-accelerating elevator? Explain.
7. If the length of a simple pendulum is doubled, what is the ratio of the new period to the old one?
6. If you want to increase the frequency of the SHM of a mass-spring system, would you increase or decrease the mass? Explain.
5. If a mass-spring system were taken to the Moon, would its period change? How about the period of a simple pendulum if taken to the Moon? Explain both.
4. A very elastic ball rattles back and forth horizontally between the walls of a box. Is this a simple harmonic motion? Explain.
3. A mass-spring system in SHM has an amplitude A and period T. How long, in units of T, does the mass take to travel a distance A? How about 2A?
2. How does the speed of a mass in SHM change as it leaves equilibrium? Explain.
1. If the amplitude of an object in SHM is doubled, how are (a) the system total energy and (b) the object’s maximum speed affected?
17. When a stretched violin string oscillates in its second harmonic mode, the standing wave pattern on the string exhibits a total of (a) 1/4 wavelength,(b) 1/2 wavelength, (c) one wavelength,(d) two wavelengths.
16. For a standing wave on a rope, the distance between adjacent antinodes is (a) 1/4 wavelength,(b) 1/2 wavelength, (c) one wavelength,(d) two wavelengths.
15. The points of zero amplitude on string standing wave are (a) nodes, (b) antinodes, (c) fundamentals,(d) resonance points.
14. For two traveling waves to form a standing wave, the waves must have the same (a) wavelength, (b) amplitude,(c) speed, (d) all of the preceding.

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