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  1. Preface
  2. Unit 1. Mechanics
    1. 1 Units and Measurement
      1. Introduction
      2. 1.1 The Scope and Scale of Physics
      3. 1.2 Units and Standards
      4. 1.3 Unit Conversion
      5. 1.4 Dimensional Analysis
      6. 1.5 Estimates and Fermi Calculations
      7. 1.6 Significant Figures
      8. 1.7 Solving Problems in Physics
      9. Chapter Review
        1. Key Terms
        2. Key Equations
        3. Summary
        4. Conceptual Questions
        5. Problems
        6. Additional Problems
        7. Challenge Problems
    2. 2 Vectors
      1. Introduction
      2. 2.1 Scalars and Vectors
      3. 2.2 Coordinate Systems and Components of a Vector
      4. 2.3 Algebra of Vectors
      5. 2.4 Products of Vectors
      6. Chapter Review
        1. Key Terms
        2. Key Equations
        3. Summary
        4. Conceptual Questions
        5. Problems
        6. Additional Problems
        7. Challenge Problems
    3. 3 Motion Along a Straight Line
      1. Introduction
      2. 3.1 Position, Displacement, and Average Velocity
      3. 3.2 Instantaneous Velocity and Speed
      4. 3.3 Average and Instantaneous Acceleration
      5. 3.4 Motion with Constant Acceleration
      6. 3.5 Free Fall
      7. 3.6 Finding Velocity and Displacement from Acceleration
      8. Chapter Review
        1. Key Terms
        2. Key Equations
        3. Summary
        4. Conceptual Questions
        5. Problems
        6. Additional Problems
        7. Challenge Problems
    4. 4 Motion in Two and Three Dimensions
      1. Introduction
      2. 4.1 Displacement and Velocity Vectors
      3. 4.2 Acceleration Vector
      4. 4.3 Projectile Motion
      5. 4.4 Uniform Circular Motion
      6. 4.5 Relative Motion in One and Two Dimensions
      7. Chapter Review
        1. Key Terms
        2. Key Equations
        3. Summary
        4. Conceptual Questions
        5. Problems
        6. Additional Problems
        7. Challenge Problems
    5. 5 Newton's Laws of Motion
      1. Introduction
      2. 5.1 Forces
      3. 5.2 Newton's First Law
      4. 5.3 Newton's Second Law
      5. 5.4 Mass and Weight
      6. 5.5 Newton’s Third Law
      7. 5.6 Common Forces
      8. 5.7 Drawing Free-Body Diagrams
      9. Chapter Review
        1. Key Terms
        2. Key Equations
        3. Summary
        4. Conceptual Questions
        5. Problems
        6. Additional Problems
        7. Challenge Problems
    6. 6 Applications of Newton's Laws
      1. Introduction
      2. 6.1 Solving Problems with Newton’s Laws
      3. 6.2 Friction
      4. 6.3 Centripetal Force
      5. 6.4 Drag Force and Terminal Speed
      6. Chapter Review
        1. Key Terms
        2. Key Equations
        3. Summary
        4. Conceptual Questions
        5. Problems
        6. Additional Problems
        7. Challenge Problems
    7. 7 Work and Kinetic Energy
      1. Introduction
      2. 7.1 Work
      3. 7.2 Kinetic Energy
      4. 7.3 Work-Energy Theorem
      5. 7.4 Power
      6. Chapter Review
        1. Key Terms
        2. Key Equations
        3. Summary
        4. Conceptual Questions
        5. Problems
        6. Additional Problems
        7. Challenge Problems
    8. 8 Potential Energy and Conservation of Energy
      1. Introduction
      2. 8.1 Potential Energy of a System
      3. 8.2 Conservative and Non-Conservative Forces
      4. 8.3 Conservation of Energy
      5. 8.4 Potential Energy Diagrams and Stability
      6. 8.5 Sources of Energy
      7. Chapter Review
        1. Key Terms
        2. Key Equations
        3. Summary
        4. Conceptual Questions
        5. Problems
        6. Additional Problems
    9. 9 Linear Momentum and Collisions
      1. Introduction
      2. 9.1 Linear Momentum
      3. 9.2 Impulse and Collisions
      4. 9.3 Conservation of Linear Momentum
      5. 9.4 Types of Collisions
      6. 9.5 Collisions in Multiple Dimensions
      7. 9.6 Center of Mass
      8. 9.7 Rocket Propulsion
      9. Chapter Review
        1. Key Terms
        2. Key Equations
        3. Summary
        4. Conceptual Questions
        5. Problems
        6. Additional Problems
        7. Challenge Problems
    10. 10 Fixed-Axis Rotation
      1. Introduction
      2. 10.1 Rotational Variables
      3. 10.2 Rotation with Constant Angular Acceleration
      4. 10.3 Relating Angular and Translational Quantities
      5. 10.4 Moment of Inertia and Rotational Kinetic Energy
      6. 10.5 Calculating Moments of Inertia
      7. 10.6 Torque
      8. 10.7 Newton’s Second Law for Rotation
      9. 10.8 Work and Power for Rotational Motion
      10. Chapter Review
        1. Key Terms
        2. Key Equations
        3. Summary
        4. Conceptual Questions
        5. Problems
        6. Additional Problems
        7. Challenge Problems
    11. 11 Angular Momentum
      1. Introduction
      2. 11.1 Rolling Motion
      3. 11.2 Angular Momentum
      4. 11.3 Conservation of Angular Momentum
      5. 11.4 Precession of a Gyroscope
      6. Chapter Review
        1. Key Terms
        2. Key Equations
        3. Summary
        4. Conceptual Questions
        5. Problems
        6. Additional Problems
        7. Challenge Problems
    12. 12 Static Equilibrium and Elasticity
      1. Introduction
      2. 12.1 Conditions for Static Equilibrium
      3. 12.2 Examples of Static Equilibrium
      4. 12.3 Stress, Strain, and Elastic Modulus
      5. 12.4 Elasticity and Plasticity
      6. Chapter Review
        1. Key Terms
        2. Key Equations
        3. Summary
        4. Conceptual Questions
        5. Problems
        6. Additional Problems
        7. Challenge Problems
    13. 13 Gravitation
      1. Introduction
      2. 13.1 Newton's Law of Universal Gravitation
      3. 13.2 Gravitation Near Earth's Surface
      4. 13.3 Gravitational Potential Energy and Total Energy
      5. 13.4 Satellite Orbits and Energy
      6. 13.5 Kepler's Laws of Planetary Motion
      7. 13.6 Tidal Forces
      8. 13.7 Einstein's Theory of Gravity
      9. Chapter Review
        1. Key Terms
        2. Key Equations
        3. Summary
        4. Conceptual Questions
        5. Problems
        6. Additional Problems
        7. Challenge Problems
    14. 14 Fluid Mechanics
      1. Introduction
      2. 14.1 Fluids, Density, and Pressure
      3. 14.2 Measuring Pressure
      4. 14.3 Pascal's Principle and Hydraulics
      5. 14.4 Archimedes’ Principle and Buoyancy
      6. 14.5 Fluid Dynamics
      7. 14.6 Bernoulli’s Equation
      8. 14.7 Viscosity and Turbulence
      9. Chapter Review
        1. Key Terms
        2. Key Equations
        3. Summary
        4. Conceptual Questions
        5. Problems
        6. Additional Problems
        7. Challenge Problems
  3. Unit 2. Waves and Acoustics
    1. 15 Oscillations
      1. Introduction
      2. 15.1 Simple Harmonic Motion
      3. 15.2 Energy in Simple Harmonic Motion
      4. 15.3 Comparing Simple Harmonic Motion and Circular Motion
      5. 15.4 Pendulums
      6. 15.5 Damped Oscillations
      7. 15.6 Forced Oscillations
      8. Chapter Review
        1. Key Terms
        2. Key Equations
        3. Summary
        4. Conceptual Questions
        5. Problems
        6. Additional Problems
        7. Challenge Problems
    2. 16 Waves
      1. Introduction
      2. 16.1 Traveling Waves
      3. 16.2 Mathematics of Waves
      4. 16.3 Wave Speed on a Stretched String
      5. 16.4 Energy and Power of a Wave
      6. 16.5 Interference of Waves
      7. 16.6 Standing Waves and Resonance
      8. Chapter Review
        1. Key Terms
        2. Key Equations
        3. Summary
        4. Conceptual Questions
        5. Problems
        6. Additional Problems
        7. Challenge Problems
    3. 17 Sound
      1. Introduction
      2. 17.1 Sound Waves
      3. 17.2 Speed of Sound
      4. 17.3 Sound Intensity
      5. 17.4 Normal Modes of a Standing Sound Wave
      6. 17.5 Sources of Musical Sound
      7. 17.6 Beats
      8. 17.7 The Doppler Effect
      9. 17.8 Shock Waves
      10. Chapter Review
        1. Key Terms
        2. Key Equations
        3. Summary
        4. Conceptual Questions
        5. Problems
        6. Additional Problems
        7. Challenge Problems
  4. A | Units
  5. B | Conversion Factors
  6. C | Fundamental Constants
  7. D | Astronomical Data
  8. E | Mathematical Formulas
  9. F | Chemistry
  10. G | The Greek Alphabet
  11. Answer Key
    1. Chapter 1
    2. Chapter 2
    3. Chapter 3
    4. Chapter 4
    5. Chapter 5
    6. Chapter 6
    7. Chapter 7
    8. Chapter 8
    9. Chapter 9
    10. Chapter 10
    11. Chapter 11
    12. Chapter 12
    13. Chapter 13
    14. Chapter 14
    15. Chapter 15
    16. Chapter 16
    17. Chapter 17
  12. Index

Check Your Understanding

17.1

Sound and light both travel at definite speeds, and the speed of sound is slower than the speed of light. The first shell is probably very close by, so the speed difference is not noticeable. The second shell is farther away, so the light arrives at your eyes noticeably sooner than the sound wave arrives at your ears.

17.2

10 dB: rustle of leaves; 50 dB: average office; 100 dB: noisy factory

17.3

Amplitude is directly proportional to the experience of loudness. As amplitude increases, loudness increases.

17.4

In the example, the two speakers were producing sound at a single frequency. Music has various frequencies and wavelengths.

17.5

Regular headphones only block sound waves with a physical barrier. Noise-canceling headphones use destructive interference to reduce the loudness of outside sounds.

17.6

When the tube resonates at its natural frequency, the wave’s node is located at the closed end of the tube, and the antinode is located at the open end. The length of the tube is equal to one-fourth of the wavelength of this wave. Thus, if we know the wavelength of the wave, we can determine the length of the tube.

17.7

Compare their sizes. High-pitch instruments are generally smaller than low-pitch instruments because they generate a smaller wavelength.

17.8

An easy way to understand this event is to use a graph, as shown below. It appears that beats are produced, but with a more complex pattern of interference.

Graph plots displacement in centimeters versus time in seconds. Three sound waves and the interference wave are shown in the graph.
17.9

If I am driving and I hear Doppler shift in an ambulance siren, I would be able to tell when it was getting closer and also if it has passed by. This would help me to know whether I needed to pull over and let the ambulance through.

Conceptual Questions

1.

Sound is a disturbance of matter (a pressure wave) that is transmitted from its source outward. Hearing is the human perception of sound.

3.

Consider a sound wave moving through air. The pressure of the air is the equilibrium condition, it is the change in pressure that produces the sound wave.

5.

The frequency does not change as the sound wave moves from one medium to another. Since the speed changes and the frequency does not, the wavelength must change. This is similar to the driving force of a harmonic oscillator or a wave on the string.

7.

The transducer sends out a sound wave, which reflects off the object in question and measures the time it takes for the sound wave to return. Since the speed of sound is constant, the distance to the object can found by multiplying the velocity of sound by half the time interval measured.

9.

The ear plugs reduce the intensity of the sound both in water and on land, but Navy researchers have found that sound under water is heard through vibrations mastoid, which is the bone behind the ear.

11.

The fundamental wavelength of a tube open at each end is 2L, where the wavelength of a tube open at one end and closed at one end is 4L. The tube open at one end has the lower fundamental frequency, assuming the speed of sound is the same in both tubes.

13.

The wavelength in each is twice the length of the tube. The frequency depends on the wavelength and the speed of the sound waves. The frequency in room B is higher because the speed of sound is higher where the temperature is higher.

15.

When resonating at the fundamental frequency, the wavelength for pipe C is 4L, and for pipes A and B is 2L. The frequency is equal to f=v/λ.f=v/λ. Pipe C has the lowest frequency and pipes A and B have equal frequencies, higher than the one in pipe C.

17.

Since the boundary conditions are both symmetric, the frequencies arefn=nv2L.fn=nv2L. Since the speed is the same in each, the frequencies are the same. If the wave speed were doubled in the string, the frequencies in the string would be twice the frequencies in the tube.

19.

The frequency of the unknown fork is 255 Hz. No, if only the 250 Hz fork is used, listening to the beat frequency could only limit the possible frequencies to 245 Hz or 255 Hz.

21.

The beat frequency is 0.7 Hz.

23.

Observer 1 will observe the highest frequency. Observer 2 will observe the lowest frequency. Observer 3 will hear a higher frequency than the source frequency, but lower than the frequency observed by observer 1, as the source approaches and a lower frequency than the source frequency, but higher than the frequency observed by observer 1, as the source moves away from observer 3.

25.

Doppler radar can not only detect the distance to a storm, but also the speed and direction at which the storm is traveling.

27.

The speed of sound decreases as the temperature decreases. The Mach number is equal to M=vsv,M=vsv, so the plane should slow down.

Problems

29.

smax=4.00nm,λ=1.72m,f=200Hz,v=343.17m/ssmax=4.00nm,λ=1.72m,f=200Hz,v=343.17m/s

31.

a. λ=68.60μm;λ=68.60μm; b. λ=360.00μmλ=360.00μm

33.

a. k=183.09m−1;k=183.09m−1;
b. ΔP=−1.11PaΔP=−1.11Pa

35.

s1=7.00nm,s2=3.00nm,kx1+ϕ=0radkx2+ϕ=1.128radk(x2x1)=1.128rad,k=5.64m−1λ=1.11m,f=306.31Hzs1=7.00nm,s2=3.00nm,kx1+ϕ=0radkx2+ϕ=1.128radk(x2x1)=1.128rad,k=5.64m−1λ=1.11m,f=306.31Hz

37.

k=5.28×103ms(x,t)=4.50nmcos(5.28×103m−1x2π(5.00MHz)t)k=5.28×103ms(x,t)=4.50nmcos(5.28×103m−1x2π(5.00MHz)t)

39.

λ=3.43mmλ=3.43mm

41.

λ=6.00msmax=2.00mmv=600m/sT=0.01sλ=6.00msmax=2.00mmv=600m/sT=0.01s

43.

(a) f=100Hz,f=100Hz, (b) λ=3.43mλ=3.43m

45.

f=3400Hzf=3400Hz

47.

a. v=5.96×103m/sv=5.96×103m/s; b. steel (from value in Table 17.1)

49.

v=363msv=363ms

51.

Δx=924mΔx=924m

53.

V=0.05m3m=392.5kgρ=7850kg/m3v=5047.54m/sV=0.05m3m=392.5kgρ=7850kg/m3v=5047.54m/s

55.

TC=35°C,v=351.58m/sΔx1=35.16m,Δx2=52.74mΔx=63.39mTC=35°C,v=351.58m/sΔx1=35.16m,Δx2=52.74mΔx=63.39m

57.

a. t5.00°C=0.0180s,t35.0°C=0.0171st5.00°C=0.0180s,t35.0°C=0.0171s; b. % uncertainty=5.00%% uncertainty=5.00%; c. This uncertainty could definitely cause difficulties for the bat, if it didn’t continue to use sound as it closed in on its prey. A 5% uncertainty could be the difference between catching the prey around the neck or around the chest, which means that it could miss grabbing its prey.

59.

1.26×103W/m21.26×103W/m2

61.

85 dB

63.

a. 93 dB; b. 83 dB

65.

1.58×1013W/m21.58×1013W/m2

67.

A decrease of a factor of 10 in intensity corresponds to a reduction of 10 dB in sound level: 120dB10dB=110dB.120dB10dB=110dB.

69.

We know that 60 dB corresponds to a factor of 106106 increase in intensity. Therefore,
IX2I2I1=(X2X1)2,so thatX2=106atm.IX2I2I1=(X2X1)2,so thatX2=106atm.
120 dB corresponds to a factor of 10121012 increase109atm(1012)1/2=103atm.109atm(1012)1/2=103atm.

71.

28.2 dB

73.

1×106km1×106km

75.

73dB70dB=3dB;73dB70dB=3dB; Such a change in sound level is easily noticed.

77.

2.5; The 100-Hz tone must be 2.5 times more intense than the 4000-Hz sound to be audible by this person.

79.

0.974 m

81.

11.0 kHz; The ear is not particularly sensitive to this frequency, so we don’t hear overtones due to the ear canal.

83.

a. v=344.08m/s,λ1=16.00m,f1=21.51Hz;v=344.08m/s,λ1=16.00m,f1=21.51Hz;
b. λ3=5.33m,f3=64.56Hzλ3=5.33m,f3=64.56Hz

85.

vstring=149.07m/s,λ3=1.33m,f3=112.08Hzλ1=vf1,L=1.53mvstring=149.07m/s,λ3=1.33m,f3=112.08Hzλ1=vf1,L=1.53m

87.

a. 22.0°C22.0°C; b. 1.01 m

89.

first overtone=180Hz;second overtone=270Hz;third overtone=360Hzfirst overtone=180Hz;second overtone=270Hz;third overtone=360Hz

91.

1.56 m

93.

The pipe has symmetrical boundary conditions;
λn=2nL,fn=nv2L,n=1,2,3λ1=6.00m,λ2=3.00m,λ3=2.00mf1=57.17Hz,f2=114.33Hz,f3=171.50Hzλn=2nL,fn=nv2L,n=1,2,3λ1=6.00m,λ2=3.00m,λ3=2.00mf1=57.17Hz,f2=114.33Hz,f3=171.50Hz

95.

λ6=0.5mv=1000m/sFT=6500Nλ6=0.5mv=1000m/sFT=6500N

97.

f=6.40kHzf=6.40kHz

99.

1.03 or 3%3%

101.

fB=|f1f2||128.3Hz128.1Hz|=0.2Hz;|128.3Hz127.8Hz|=0.5Hz;|128.1Hz127.8Hz|=0.3HzfB=|f1f2||128.3Hz128.1Hz|=0.2Hz;|128.3Hz127.8Hz|=0.5Hz;|128.1Hz127.8Hz|=0.3Hz

103.

vA=135.87m/s,vB=141.42m/s,λA=λB=0.40mΔf=15.00HzvA=135.87m/s,vB=141.42m/s,λA=λB=0.40mΔf=15.00Hz

105.

v=155.54m/s,fstring=971.17Hz,n=16.23fstring=1076.83Hz,n=18.00v=155.54m/s,fstring=971.17Hz,n=16.23fstring=1076.83Hz,n=18.00
The frequency is 1076.83 Hz and the wavelength is 0.14 m.

107.

f2=f1±fB=260.00Hz±1.50Hz,so thatf2=261.50Hzorf2=258.50Hzf2=f1±fB=260.00Hz±1.50Hz,so thatf2=261.50Hzorf2=258.50Hz

109.

face=f1+f22;fB=f1f2(assumef1>f2)face=(fB+f2)+f22f2=4099.750Hzf1=4100.250Hzface=f1+f22;fB=f1f2(assumef1>f2)face=(fB+f2)+f22f2=4099.750Hzf1=4100.250Hz

111.

a. 878 Hz; b. 735 Hz

113.

3.79×103Hz3.79×103Hz

115.

a. 12.9 m/s; b. 193 Hz

117.

The first eagle hears 4.23×103Hz.4.23×103Hz. The second eagle hears 3.56×103Hz.3.56×103Hz.

119.

vs=31.29m/sfo=1.12kHzvs=31.29m/sfo=1.12kHz

121.

An audible shift occurs when fobsfs1.003fobsfs1.003; fobs=fsvvvsfobsfs=vvvsvs=0.990m/sfobs=fsvvvsfobsfs=vvvsvs=0.990m/s

123.

θ=30.02°vs=680.00m/stanθ=yvst,t=21.65sθ=30.02°vs=680.00m/stanθ=yvst,t=21.65s

125.

sinθ=1M,θ=56.47°y=9.31kmsinθ=1M,θ=56.47°y=9.31km

127.

s1=6.34nms2=2.30nmkx1+ϕ=0radkx2+ϕ=1.20radk(x2x1)=1.20radk=3.00m−1ω=1019.62s−1s1=smaxcos(kx1ϕ)ϕ=5.66rads(x,t)=6.30nmcos(3.00m−1x1019.62s−1t+5.66)s1=6.34nms2=2.30nmkx1+ϕ=0radkx2+ϕ=1.20radk(x2x1)=1.20radk=3.00m−1ω=1019.62s−1s1=smaxcos(kx1ϕ)ϕ=5.66rads(x,t)=6.30nmcos(3.00m−1x1019.62s−1t+5.66)

Additional Problems

129.

vs=346.40m/svs=346.40m/s;
λn=2nLfn=vsλnλ1=1.60mf1=216.50Hzλ2=0.80mf1=433.00Hzλn=2nLfn=vsλnλ1=1.60mf1=216.50Hzλ2=0.80mf1=433.00Hz

131.

a. λ6=0.40mv=57.15msf6=142.89Hzλ6=0.40mv=57.15msf6=142.89Hz; b. λs=2.40mλs=2.40m

133.

v=344.08msvA=29.05ms,vB=33.52m/sfA=961.18Hz,fB=958.89HzfA,beat=161.18Hz,fB,beat=158.89Hzv=344.08msvA=29.05ms,vB=33.52m/sfA=961.18Hz,fB=958.89HzfA,beat=161.18Hz,fB,beat=158.89Hz

135.

v=345.24msv=345.24ms; a. I=31.62μWm2I=31.62μWm2; b. I=0.16μWm2I=0.16μWm2; c. smax=104.39μmsmax=104.39μm; d. smax=7.43μmsmax=7.43μm

137.

fAfD=v+vsvvs,(vvs)fAfD=v+vs,v=347.39msTC=27.70°fAfD=v+vsvvs,(vvs)fAfD=v+vs,v=347.39msTC=27.70°

Challenge Problems

139.

x2+d2x=λ,x2+d2=(λ+x)2x2+d2=λ2+2xλ+x2,d2=λ2+2xλx=d2(vf)22vfx2+d2x=λ,x2+d2=(λ+x)2x2+d2=λ2+2xλ+x2,d2=λ2+2xλx=d2(vf)22vf

141.

a. For maxima Δr=dsinθdsinθ=nλn=0,±1,±2....,θ=sin−1(nλd)n=0,±1,±2....Δr=dsinθdsinθ=nλn=0,±1,±2....,θ=sin−1(nλd)n=0,±1,±2....
b. For minima, Δr=dsinθdsinθ=(n+12)λn=0,±1,±2....θ=sin−1((n+12)λd)n=0,±1,±2....Δr=dsinθdsinθ=(n+12)λn=0,±1,±2....θ=sin−1((n+12)λd)n=0,±1,±2....

143.

a. vstring=160.73ms,fstring=535.77Hzvstring=160.73ms,fstring=535.77Hz; b. ffork=512Hzffork=512Hz; c. ffork=nFTμ2L,FT=141.56Nffork=nFTμ2L,FT=141.56N

145.

a. f=268.62Hzf=268.62Hz; b. Δf12ΔFTFTf=1.34HzΔf12ΔFTFTf=1.34Hz

147.

a. v=466.07msv=466.07ms; b. λ9=51.11mmλ9=51.11mm; c. f9=9.12kHzf9=9.12kHz;
d. fsound=9.12kHzfsound=9.12kHz; e. λair=37.86mmλair=37.86mm

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