Deck 15: Wave Motion

Question 1

Describe the phenomenon known as refraction

Answer 1

When any wave strikes a boundary, some of the energy is reflected and some is transmitted or absorbed. When a two- or three-dimensional wave traveling in one medium crosses a boundary into a medium where its speed is different, the transmitted wave may move in a different direction than the incident wave.

Question 2

Write an expression for a harmonic wave that has an amplitude of 18 cm, a wavelength of 2.0 m, and propagates to the left at 15 m/s.

Answer 2

y(x,t) = (18 cm) cos[(3.1 m^-1)x + (47 s^-1)t] or
y(x,t) = (18 cm) cos[((2π/2.0)m^-1)x + ((2π × 7.5) s^-1)t]

Question 3

List and describe the two types of waves.

Answer 3

In a transverse wave, the vibration of the particles of the medium is perpendicular to the motion of the wave itself. In a longitudinal wave, the vibration of the particles of the medium is along the direction of the wave's motion.

Question 4

List and describe the two types of interference.

Question 5

If two waves pass through the same region of space, they continue to move independently of one another.

Question 6

The velocity of a transverse wave on a stretched string or cord depends only on the tension in the cord.

Question 7

A wave pulse on a string whose end is fixed is reflected without inversion.

Question 8

Both transverse and longitudinal waves are produced when an earthquake occurs.

Question 9

For a periodic process, the number of cycles per unit time is called the

A)amplitude.
B)wavelength.
C)frequency.
D)period.
E)pulse.

Question 10

The velocity of a longitudinal wave traveling down a solid rod depends on both the elastic modulus of the material and its density.

Question 11

The velocity of a wave is independent of the properties of the medium in which it travels.

Question 12

Give three examples of three-dimensional waves.

Question 13

The velocity of a longitudinal wave traveling in a liquid or a gas depends only on the density of the fluid.

Question 14

The time for one cycle of a periodic process is called the

A)amplitude.
B)wavelength.
C)frequency.
D)period.
E)pulse.

Question 15

The energy transported by a wave is proportional to the amplitude of the wave.

Question 16

The energy transported by a wave is proportional to the square of the frequency of the wave.

Question 17

Describe the phenomenon known as diffraction.

Question 18

Give at least one example of each of the following:
(a) longitudinal standing wave.
(b) transverse standing wave.

Question 19

State the principle of superposition.

Question 20

A wave pulse on a string whose end is free is reflected without inversion.

Question 21

A wave pulse traveling to the right along a thin cord reaches a discontinuity where the rope becomes thinner and lighter. What is the orientation of the reflected and transmitted pulses?

A)both are right side up
B)the reflected pulse returns right side up while the transmitted pulse is inverted
C)the reflected pulse returns inverted while the transmitted pulse is right side up
D)both are inverted
E)It is impossible to predict.

Question 22

FIGURE 15-2
Fig. 15-2 shows the displacement of a wave at a given position as a function of time and the displacement of the same wave at a given time as a function of position. Determine the frequency of the wave.

A)4.0 Hz
B)0.50 Hz
C)3.0 Hz
D)0.33 Hz
E)0.25 Hz

Question 23

FIGURE 15-2
Fig. 15-2 shows the displacement of a wave at a given position as a function of time and the displacement of the same wave at a given time as a function of position. Determine the speed of the wave.

A)3.0 m/s
B)0.75 m/s
C)0.66 cm/s
D)1.5 m/s
E)2.00 cm/s

Question 24

FIGURE 15-1
In Fig. 15-1, the wavelength is

A)8 m.
B)4 m.
C)2 m.
D)1 m.
E)cannot be determined from the given information.

Question 25

A wave pulse traveling to the right along a thin cord reaches a discontinuity where the rope becomes thicker and heavier. What is the orientation of the reflected and transmitted pulses?

A)both are right side up
B)the reflected pulse returns right side up while the transmitted pulse is inverted
C)the reflected pulse returns inverted while the transmitted pulse is right side up
D)both are inverted
E)It is impossible to predict.

Question 26

For vibrational motion, the maximum displacement from the equilibrium point is called the

A)amplitude.
B)wavelength.
C)frequency.
D)period.
E)pulse.

Question 27

Four waves are described by the following expressions, where distances are measured in meters and times in seconds. I y = 0.12 cos(3x - 21t)II y = 0.15 sin(6x + 42t)III y = 0.13 cos(6x + 21t)IV y = -0.23 sin(3x - 42t)Which of these waves travel in the +x direction?

A)I and II
B)I and III
C)II and IV
D)I and IV
E)II and III

Question 28

Two in phase coherent sources emitting harmonic waves of wavelength λ are separated by a distance d. What is the minimum value of d for which destructive interference occurs everywhere along the line that passes through the locations of the two sources?

A)λ/2
B)λ
C)zero
D)2λ
E)λ/4

Question 29

FIGURE 15-2
A harmonic wave has a wavelength of 2.0 m and a frequency of 5.0 Hz. What is the speed of the wave?

A)10 m/s
B)0.40 m/s
C)0.50 m/s
D)0.10 m/s
E)2.5 m/s

Question 30

Two wave pulses pass each other on a string. The one traveling toward the right has a positive amplitude, while the one traveling toward the left has an equal amplitude in the negative direction. At the point that they occupy the same region of space at the same time

A)constructive interference occurs.
B)destructive interference occurs.
C)a standing wave is produced.
D)a traveling wave is produced.
E)a wave pulse is produced.

Question 31

Two wave pulses with equal positive amplitudes pass each other on a string, one is traveling toward the right and the other toward the left. At the point that they occupy the same region of space at the same time

A)constructive interference occurs.
B)destructive interference occurs.
C)a standing wave is produced.
D)a traveling wave is produced.
E)a wave pulse is produced.

Question 32

Four waves are described by the following expressions, where distances are measured in meters and times in seconds. I y = 0.12 cos(3x - 21t)II y = 0.15 sin(6x + 42t)III y = 0.13 cos(6x + 21t)IV y = -0.23 sin(3x - 42t)Which of these waves have the same speed?

A)I and II
B)I and III
C)II and III
D)III and IV
E)II and IV

Question 33

In a one-dimensional system, a standing wave is the result of ________

A)two equal amplitude, equal wavelength waves traveling in the same direction.
B)two waves of different amplitude, but equal wavelength traveling in the same direction.
C)two waves of different frequency, but equal amplitude traveling in the same direction.
D)two waves of different frequency, but equal amplitude traveling in opposite directions.
E)two equal amplitude, equal wavelength waves traveling in opposite directions.

Question 34

FIGURE 15-2
Fig. 15-2 shows the displacement of a wave at a given position as a function of time and the displacement of the same wave at a given time as a function of position. Determine the wavelength of the wave.

A)2.0 cm
B)3.0 m
C)2.0 m
D)4.0 m
E)1.5 m

Question 35

The wavelengths corresponding to the harmonics of a string with fixed ends can be found by saying that the length of the string must be equal to

A)an odd number of quarter-wavelengths.
B)an odd number of third-wavelengths.
C)an odd number of half-wavelengths.
D)an integer number of half-wavelengths.
E)an integer number of wavelengths.

Question 36

A harmonic wave travels with a speed of 200 m/s and has a wavelength of 0.800 m. What is the frequency of the wave?

A)25.0 Hz
B)40.0 Hz
C)125 Hz
D)80.0 Hz
E)250 Hz

Question 37

Four waves are described by the following expressions, where distances are measured in meters and times in seconds. I y = 0.12 cos(3x - 21t)II y = 0.15 sin(6x + 42t)III y = 0.13 cos(6x + 21t)IV y = -0.23 sin(3x - 42t)Which of these waves have the same period?

A)I and III, and also II and IV
B)I and IV, and also II and III
C)I and II, and also III and IV
D)All of them have the same period.
E)They all have different periods.

Question 38

Consider the wave equation below: = where A and B are positive constants. What is the speed of waves described by this equation?

A)
B)B²/A²
C)1/
D)
E)

Question 39

Two in phase coherent sources emitting harmonic waves of wavelength λ are separated by a distance d. What is the minimum non-zero value of d for which constructive interference occurs everywhere along the line that passes through the locations of the two sources?

A)λ/4
B)λ
C)2λ
D)λ/2
E)4λ

Question 40

FIGURE 15-1
In Fig. 15-1, the frequency is

A)0.5 Hz.
B)1 Hz.
C)2 Hz.
D)4 Hz.
E)cannot be determined from the given information.

Question 41

A wave has an amplitude 20.0 cm, a wavelength 3.00 m, and the wave travels 60.0 m in 12.0 s. What is the frequency of the wave?

A)8.33 Hz
B)250 Hz
C)0.500 Hz
D)1.67 Hz
E)150 Hz

Question 42

A wave has a period 2.00 s, an amplitude 20.0 cm, and a wavelength 3.00 m. What is the speed of the wave?

A)10.0 cm/s
B)1.50 m/s
C)340 m/s
D)0.100 cm/s
E)0.667 m/s

Question 43

A 6.00-m long rope is under a tension of 600 N. Waves travel along this rope at 40.0 m/s. What is the mass of the rope?

A)1.00 kg
B)1.25 kg
C)2.25 kg
D)2.50 kg
E)1.12 kg

Question 44

Traveling waves are created on a rope that has a mass per length 0.200 kg/m that is stretched with a tension of 400 N. If the end of the rope is moved up and down with simple harmonic motion with amplitude 30.0 cm and a period 1.40 s, how much work is done in one period of the motion?

A)133 J
B)400 J
C)267 J
D)11.3 J
E)No work is done because the tension pulls outward along the rope, but the end of the rope moves perpendicular to the rope.

Question 45

Which of the following is a solution to the wave equation:

A)z(x,t) = Acos[k(x - Ct)]
B)z(x,t) = Acos[k(x - C^2t)]
C)z(x,t) = Acos[k(x - t/C)]
D)z(x,t) = Acos[k(x - t)]
E)z(x,t) = Acos[k(x - t/ )]

Question 46

The vertical displacement of a string is given by y(x,t) = (6.00 mm) cos[(3.25 m^-1)x - (7.22 s^-1)t]. What is the period of the wave?

A)7.22 s
B)1.93 s
C)0.870 s
D)0.308 s
E)0.139 s

Question 47

The speed of waves on a thin wire is 150 m/s. The density of the material that the wire is made of is 5000 kg/m³. The wire has a 0.500 mm diameter circular crosssection. What is the tension that the wire is under?

A)76.2 N
B)22.1 N
C)88.4 N
D)0.147 N
E)56.7 N

Question 48

A tsunami, an ocean wave generated by an earthquake, propagates along the open ocean at 700 km/hr and has a wavelength of 750 km. What is the frequency of the waves in such a tsunami?

A)0.00026 Hz
B)1.1 Hz
C)1100 Hz
D)930 Hz
E)0.93 Hz

Question 49

The vertical displacement of a string is given by y(x,t) = (6.00 mm) cos[(3.25 m^-1)x - (7.22 s^-1)t]. What is the amplitude of the wave?

A)6.00 mm
B)12.0 mm
C)3.00 mm
D)2.00 mm
E)None of the other choices is correct.

Question 50

An earthquake generates three kinds of waves: surface waves (L-waves), which are the slowest and weakest, shear (S) waves, which are transverse waves and carry most of the energy, and pressure (P) waves, which are longitudinal waves and are the fastest. People do not generally feel the P waves, but animals seem to be sensitive to them. Take the density of the material through which these waves travel to be 2.0 × 10³ kg/m³, the Young's modulus to be 9.8 × 10¹⁰ N/m², and the shear modulus to be 3.2 × 10¹⁰ N/m². A person reports that her dog started barking 30 seconds "before the earthquake." Approximately how far away was the origin of the earthquake?

A)180 km
B)280 km
C)140 km
D)90 km
E)360 km

Question 51

Ocean tides are waves that have a period of 12 hours and a speed of 750 km/hr. What is their wavelength?

A)9000 km
B)32,400 km
C)9000 m
D)32,400 m
E)2,500 m

Question 52

Waves travel along a 100-m length of string with a mass of 55 g, which is held taut by a tension of 75 N. What is the speed of the waves?

A)3700 m/s
B)370 m/s
C)37 m/s
D)0.37 m/s
E)3.7 m/s

Question 53

A small town has decided to forego the use of electrical power and send energy through town via mechanical waves on ropes. They use rope with a mass per length of 1.50 kg/m under 6000 N tension. If they are limited to a wave amplitude of 0.500 m, what must be the frequency of waves necessary to transmit power at the average rate of 2.00 kW?

A)24.8 Hz
B)169 Hz
C)60.0 Hz
D)2.07 Hz
E)2.00 kHz

Question 54

The density of aluminum is 2.7 × 10³ kg/m³. The speed of longitudinal waves in an aluminum rod is measured to be 5.1 × 10³ m/s. What is the value of Young's modulus for aluminum?

A)7.0 × 10¹⁰ N/m²
B)7.0 × 10⁷ N/m²
C)2.2 × 10¹¹ N/m²
D)2.2 × 10⁹ N/m²
E)1.4 × 10⁷ N/m²

Question 55

The vertical displacement of a string is given by y(x,t) = (6.00 mm) cos[(3.25 m^-1)x - (7.22 s^-1)t]. What is the speed of the wave?

A)0.450 m/s
B)1.41 m/s
C)2.22 m/s
D)3.16 m/s
E)23.5 m/s

Question 56

What is the period of a wave described by the following function: y(x,t) = (2.00 m)cos[(3.00 m^-1)x + (5.00 s^-1)t]

A)0.333 s
B)0.200 s
C)5.00 s
D)1.26 s
E)2.09 s

Question 57

Periodic waves with a period of 0.026 s travel along a rod at 1200 m/s. What is the wave number k of the waves?

A)5.0 m^-1
B)31 m^-1
C)6.9 m^-1
D)0.20 m^-1
E)68 m^-1

Question 58

What is the period of a wave described by the following function? y(x,t) = (2.00 m)cos[(6.00 m^-1)x + (10.00 s^-1)t] + (2.00 m)cos[(3.00 m^-1)x + (5.00 s^-1)t]

A)0.628 s
B)5.00 s
C)1.26 s
D)10.0 s
E)This is not a periodic function, so it does not have a period.

Question 59

A wave is described by the function y(x,t) = (3.00 cm)cos[( 3.00 m^-1)x + ( 4.00 s^-1)t]. What is the wavelength of this wave?

A)2.09 m
B)3.00 m
C)0.333 m
D)0.250 m
E)1.57 m

Question 60

What is the wavelength of a wave described by the following function: y(x,t) = (2.00 m)cos[(3.00 m^-1)x + (5.00 s^-1)t]

A)2.09 m
B)3.00 m
C)5.00 m
D)1.26 m
E)0.333 m

Question 61

Two waves are traveling through a medium simultaneously. The first wave is described by y₁(x,t) = Acos(kx-ωt) and the second wave is described by y₂(x,t) = 2A sin(kx-ωt). If the result of the superposition is written in the form y(x,t) = B cos(kx-ωt + φ), determine B in terms of A.

A)3A
B) A
C)A/3
D) A
E)A

Question 62

A 2.00-m long piano wire with a mass per unit length of 12.0 g/m is under a tension of 8.00 kN. What is the frequency of the fundamental mode?

A)204 Hz
B)102 Hz
C)408 Hz
D)510 Hz
E)153 Hz

Question 63

Two waves travel simultaneously through the same medium. The first wave is described by y₁(x,t) = (2.00 cm)cos[kx-ωt] and the second wave by y₂(x,t) = (3.00 cm)sin(kx-ωt). If the resulting superposition can be written as y(x,t) = Ccos(kx-ωt + δ), what is the value of δ?

A)0.983
B)1.50
C)0.833
D)0.782
E)0.667

Question 64

The mass density of platinum is 21.4 × 10³ kg/m³. A platinum wire with a radius of 0.500 mm, 1.20 m long, fixed at both ends has a frequency of vibration for its third harmonic equal to 512 Hz. What is the tension in the wire?

A)4.00 kN
B)2.00 kN
C)2.82 kN
D)1.41 kN
E)1.00 kN

Question 65

Two waves travel simultaneously through the same medium. The first wave is described by y₁(x,t) = (2.00 cm)cos[kx-ωt] and the second wave by y₂(x,t) = (3.00 cm)cos(kx-ωt+δ). If the resulting wave has an amplitude 4.00 cm, what is a possible value of δ?

A)0.782 rad
B)0.250 rad
C)0.644 rad
D)0.833 rad
E)1.32 rad

Question 66

Two waves travel simultaneously through the same medium. The first wave is described by y₁(x,t) = Acos(kx-ωt) and the second wave by y₂(x,t) = A cos(kx-ωt + φ). If the amplitude of the resulting superposition is A/2, what are the possible values of φ?

A)π/6, -π/6
B)π/3, -π/3
C)π/8, -π/8
D)60°, -60°
E)π/4, -π/4

Question 67

At a location that is 3.00 m from wave source A and 4.20 m from wave source B, constructive interference occurs. Source A and source B are coherent and in phase. What is the maximum wavelength of the waves?

A)2.40 m
B)12.6 m
C)0.60 m
D)1.20 m
E)There is no maximum wavelength.

Question 68

A 60.0-cm long string with a mass 8.00 g has a tension 200 N. What is the fundamental frequency of this string?

A)38.7 Hz
B)1500 Hz
C)56.7 Hz
D)102 Hz
E)3.75 Hz

Question 69

A guitar string is supposed to have a fundamental frequency 256 Hz. It currently has a fundamental frequency 248 Hz. What percentage increase in tension is required to bring the guitar string into tune?

A)3.13%
B)6.56%
C)1.60%
D)6.15%
E)3.23%

Question 70

Two traveling waves have the forms z₁ = A sin(kx - ωt), z₂ = A sin(kx + ωt ) Express their superposition in the form of a standing wave.

A)2A cos(kx) cos( ωt )
B)2A sin(kx) cos( ωt )
C)2A sin(kx) sin( ωt )
D)A sin[(kx )² - (ωt )²]
E)2A cos(kx) sin( ωt )

Question 71

Two waves travel simultaneously through the same medium. The first wave is described by y₁(x,t) = (2.00 cm)cos[kx-ωt] and the second wave by y₂(x,t) = (3.00 cm)sin(kx-ωt). What is the amplitude of the resulting wave?

A)1.00 cm
B)2.50 cm
C)3.61 cm
D)5.00 cm
E)3.94 cm

Question 72

At a location that is 3.00 m from wave source A and 4.20 m from wave source B, destructive interference occurs. Source A and source B are coherent and in phase. What is the maximum wavelength of the waves?

A)0.60 m
B)1.20 m
C)12.6 m
D)1.40 m
E)2.40 m

Question 73

What is the speed of the wave described by y(x,t) = A cos(x² + 2Bxt +B^2t2)

A)B/2
B)B
C)2Bx
D)B²
E)The function given is not a solution to the wave equation.

Question 74

Two waves travel simultaneously through the same medium. The first wave is described by y₁(x,t) = Acos(kx-ωt) and the second wave by y₂(x,t) = B sin(kx-ωt). If the resulting superposition can be written as y(x,t) = C cos(kx-ωt + π/5), what is the value of A/B?

A)sin(π/5)
B)cos(π/5)
C)cot(π/5)
D)sec(π/5)
E)tan(π/5)