1. Waves and Sound Solutions
The Properties of Waves
Vibration
Transverse waves: the energy and motion are placed at 90 degrees to each other. i.e the vibration is perpendicular to the propagation Propagation
Compressional waves: the energy and motion in the same direction. i.e the vibration is parallel to the propagation Propagation
V
V
Vibration
• Wavelength: Distance Between two successive points that are in phase. (λ)
• Velocity(v) of a wave= Frequency (f) times the wavelength (λ)
• Period (T) The time it takes for motion to repeat itself in seconds
• Frequency (F) The number of times the wave repeats in a second. Measured in Hertz (Hz)
• Amplitude (A) the power or size of the wave. Measured by the displacement from the “rest” position
Earthquake Waves Demo
http://www.classzone.com/books/earth_science/terc/content/visualizations/es1002/es1002page0
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1. Waves and Sound Solutions
Waves
Light
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1. Waves and Sound Solutions
• What is the wavelength of a sound wave whose speed
is 330 m/s and whose frequency is 660 Hz.
V=fλ
λ = v/f
λ = .5 m
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1. Waves and Sound Solutions
The 4 Wave Behaviors
1. Reflection: When a wave travels to a new medium, part of the wave is redirected at the same frequency at the same angle from the normal to the surface of the redirection. The angle of incidence = the angle of Reflection θι= θR 2. Refraction: When a wave travels from one medium to a second medium, The original wave is redirected at the different angle (bend) from the normal to the surface. The frequency remains the same but the speed and wavelength changes. For light waves: The index of refraction, n, determines the amount of change in frequency and angle. (bending the wave)
3. Diffraction: The spreading of a wave around an obstacle in the same medium
4. Interference: The Addition of waves can add (Constructive) or subtract (destructive). Standing waves are a result of waves combining in phase after the incident wave reflects off a boundary. 4
1. Waves and Sound Solutions
Which points in the choices have the same displacement but are moving in opposite directions?
Reason Points A and C show the same displacement, but the energy in point A is moving up, while the energy in C is moving down. These points are out of phase by 180 degrees.
1
0
3
2
4
5
6
8
7
9
11
10
13
12
14
15
0°
0
1
2
3
4
5
Observe the crests and troughs.
Reason The crests and troughs of both waves, or magnitudes of maximum displacement, indicate that both waves have the same amplitude.
3. When air is blown across the top of an open water bottle, air molecules in the bottle vibrate at a particular frequency and sound is produced. This phenomenon is called
1. diffraction
2. refraction
3. resonance
4. the Doppler effect
“Sympathetic vibrations”
Reason Resonance occurs when a vibrating object induces another to vibrate. This will happen when both of the objects have the same natural vibrating frequency.
4. As a car approaches a pedestrian crossing the road, the driver blows the horn. Compared to the sound wave emitted by the horn, the sound wave detected by the pedestrian has a:
1. higher frequency and a lower pitch
This is an example of a Doppler Effect.
2. higher frequency and a higher pitch
Reason 3. lower frequency and a higher pitch
4. lower frequency and a lower pitch
The Doppler Effect occurs when an observer or a source is moving. The observed frequency increases when the source of vibration is approaching the observer such as in this question. The pedestrian would detect a higher frequency and a higher pitch.
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1. Waves and Sound Solutions
This is an example of constructive interference.
Reason This is an example of constructive interference where each pulse is in phase and will superimpose on each other. The two pulses will meet and their amplitudes will add, creating a displacement of 6 cm.
6. When x­ray radiation and infrared radiation are traveling in a vacuum, they have the same
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1. speed
All light speed, c = 3x10 m/s
2. frequency
3. wavelength
4. energy per photon
7. A beam of light has a wavelength of 4.5 × 10−7 meter in a vacuum. The frequency of this light is
1. 1.5 × 10−15 Hz
2. 4.5 × 10−7 Hz
3. 1.4 × 102 Hz
4. 6.7 × 1014 Hz
8. What is the period of a sound wave having a frequency of 340. hertz?
1. 3.40 × 102 s
2. 1.02 × 100 s
3. 9.73 × 10−1 s
4. 2.94 × 10−3 s
9. A boy pushes his sister on a swing. What is the frequency of oscillation of his sister on the swing if the boy counts 90. complete swings in 300. seconds?
1. 0.30 Hz
2. 2.0 Hz
3. 1.5 Hz
4. 18 Hz
10. As a monochromatic light ray passes from air into water, two characteristics of the ray that will not change are
1. wavelength and period
Reason 2. frequency and period
The frequency of a wave, or the number of waves passing a point per unit of time, is determined by the source of the waves. Therefore, the frequency of the wave will not change when it enters from one medium to another, nor will its period, which is the time for one complete cycle.
3. wavelength and speed
4. frequency and speed
11. Transverse waves are to radio waves as longitudinal waves are to
1. light waves
2. microwaves
Radio waves are transverse waves, and sound waves are longitudinal waves.
3. ultraviolet waves
4. sound waves
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1. Waves and Sound Solutions
Think diffraction!
Reason Diagram 1 correctly shows the diffraction or the spreading of a wave with the correct (same) wavelength as it passes through a narrow opening.
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Hint How would the waves superimpose on each other?
Reason In the region between A and B, the two waves are superimposed. The crest of one wave would meet the crest of the other wave, resulting in constructive interference.
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14. A physics student takes her pulse and determines that her heart beats periodically 60 times in 60 seconds. The period of her heartbeat is
1. 1 Hz
Hint 2. 60 Hz
One heartbeat is one complete cycle. f = event/ second
3. 1 s
Reason 4. 60 s
The period is the time for one complete cycle. Since there are 60 heartbeats in 60 seconds, then one heartbeat would occur in one second (1 s).
15. Sound waves are produced by the horn of a truck that is approaching a stationary observer. Compared to the sound waves detected by the driver of the truck, the sound waves detected by the observer have a greater
1. wavelength
2. frequency
3. period
4. speed
This Doppler effect is produced by the truck and the sound waves both moving towards the observer.
Reason The Doppler effect is the observed change in the frequency of a moving object. In this case, since both the truck and sound waves are moving towards the observer, the observer will perceive that the sound has greater frequency.
16. One vibrating 256­hertz tuning fork transfers energy to another 256­hertz tuning fork, causing the second tuning fork to vibrate. This phenomenon is an example of
1. diffraction
This phenomenon is sometimes referred to as “sympathetic vibrations.”
2. reflection
Reason 3. refraction
Resonance is the term used to describe what occurs when a vibrating object is forced to vibrate at one of its natural frequencies by another vibrating object.
4. resonance
17. A distance of 1.0 × 10−2 meter separates successive crests of a periodic wave produced in a shallow tank of water. If a crest passes a point in the tank every 4.0 × 10−1 second, what is the speed of this wave?
1. 2.5 × 10−4 m/s
2. 4.0 × 10−3 m/s
3. 2.5 × 10−2 m/s
4. 4.0 × 10−1 m/s
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1. Waves and Sound Solutions
Hint Points on a periodic wave that have the same amplitude and are moving in the same direction are said to be in phase.
Reason In the choices given, only points D and G, choice 4, are out of phase. Although they have the same amplitude, the points are moving in opposite directions. At point D, the wave is moving down below the equilibrium position (axis), while at point G, it is moving up above the equilibrium position (axis).
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19. A sound wave traveling eastward through air causes the air molecules to
1. vibrate east and west
Sound is a longitudinal wave.
2. vibrate north and south
Reason 3. move eastward, only
4. move northward, only
In longitudinal waves, such as sound waves, the particles of the medium vibrate back and forth in the direction that the wave is traveling. So, the particles in a sound wave traveling east would vibrate east and west.
20. The energy of a sound wave is most closely related to the wave’s
1. frequency
2. amplitude
3. wavelength
4. speed
21. Which statement describes a characteristic common to all electromagnetic waves and mechanical waves?
1. Both types of waves travel at the same speed. (False)
2. Both types of waves require a material medium for propagation. (F)
3. Both types of waves propagate in a vacuum. (F)
4. Both types of waves transfer energy.
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Constructive interference occurs when two waves in phase meet. A crest of one wave meets a crest of the other wave, and a trough of one wave meets a trough of the other.
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23. A wave passes through an opening in a barrier. The amount of diffraction experienced by the wave depends on the size of the opening and the wave’s
1. amplitude
2. wavelength
3. velocity
4. phase
Diffraction is the spreading of a wave as it passes through an opening. Reason The amount of diffraction, spreading through an opening, depends on the ratio between the opening and the wavelength of the wave.
24. While sitting in a boat, a fisherman observes that two complete waves pass by his position every 4 seconds. What is the period of these waves?
1. 0.5 s
2. 2 s
3. 8 s
4. 4 s
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1. Waves and Sound Solutions
The Doppler Effect occurs when a wave source is moving or the observer is moving. The observed frequency increases when the source of vibrations is moving towards the observer. The observed frequency decreases while the source is moving away from the observer or the observer is moving away from the source.
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26. Ultrasound is a medical technique that transmits sound waves through soft tissue in the human body. Ultrasound waves can break kidney stones into tiny fragments, making it easier for them to be excreted without pain. The shattering of kidney stones with specific frequencies of sound waves is an application of which wave phenomenon?
1. the Doppler effect
2. reflection
3. refraction
4. resonance
The ultrasound waves make the kidney stones vibrate. Reason Resonance is the phenomenon that forces an object to vibrate at one of its natural frequencies.
27. What is the wavelength of a 2.50­kilohertz sound wave traveling at 326 meters per second through air?
1. 0.130 m
2. 1.30 m
3. 7.67 m
4. 130. m
28. What is characteristic of both sound waves and electromagnetic waves?
1. They require a medium.
2. They transfer energy.
3. They are mechanical waves.
4. They are longitudinal waves.
29. A tuning fork vibrates at a frequency of 512 hertz when struck with a rubber hammer. The sound produced by the tuning fork will travel through the air as a
1. longitudinal wave with air molecules vibrating parallel to the direction of travel
2. transverse wave with air molecules vibrating parallel to the direction of travel
3. longitudinal wave with air molecules vibrating perpendicular to the direction of travel
4. transverse wave with air molecules vibrating perpendicular to the direction of travel
30. The wavelength of a wave doubles as it travels from medium A into medium B. Compared to the wave in medium A, the wave in medium B has
1. half the speed
2. twice the speed
3. half the frequency
The frequency of the wave is determined by the source of the wave. As the wavelength doubles, the speed of the wave will also double to maintain this fixed frequency.
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1. Waves and Sound Solutions
The wave fronts must pass through the narrow opening.
Reason Diffraction is the spreading of a wave into a region behind a barrier as it comes through a narrow opening. The wave fronts in the diagram must pass through the narrow opening and then spread into the region behind the opening to point P.
Reason In a transverse wave, the wave vibrations are at right angles to the direction of wave movement. The diagram shows a trough followed by a crest. The movement of the cork is vertical while the wave moves across horizontally. As the trough passes the cork, the cork will move down. Then as the crest passes, the cork will move up. Then the cork will move down as the wave is past
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33. A 256­hertz vibrating tuning fork is brought near a non­vibrating 256­hertz tuning fork. The second tuning fork begins to vibrate. Which phenomenon causes the non­vibrating tuning fork to begin to vibrate?
1. resistance
2. resonance
3. refraction
4. reflection
Reason Resonance is the effect that occurs when an object is forced to vibrate at one of its natural frequencies by another vibrating object. This is sometimes called “sympathetic vibration.”
34. Which statement correctly describes one characteristic of a sound wave?
1. A sound wave can travel through a vacuum.
2. A sound wave is a transverse wave.
3. The amount of energy a sound wave transmits is directly related to the wave’s amplitude.
4. The amount of energy a sound wave transmits is inversely related to the wave’s frequency.
35. What is the wavelength of a 256­hertz sound wave in air at STP?
1. 1.17 × 106 m
2. 1.29 m
3. 0.773 m
From the reference table, the speed of sound in the air at STP is 3.31 × 102 m/s. Since Hertz is a unit of frequency, we can apply the wave equation:
4. 8.53 × 10–7 m
36. What is the period of a water wave if 4.0 complete waves pass a fixed point in 10. seconds?
1. 0.25 s
2. 0.40 s
3. 2.5 s
The frequency, f, of the wave is the number of cycles per unit of time. The period, T, is the reciprocal of the frequency.
4. 4.0 s
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1. Waves and Sound Solutions
How is amplitude related to the magnitude of the wave crest?
Reason The amplitude of a wave is the magnitude of the maximum displacement of the particle. In this wave diagram, we can read the maximum positive displacement (height of the crest) is 4 cm.
A node is a point on a standing wave where there is no motion.
Reason In the standing wave in the diagram, there are 5 nodes, points where the crest of one wave meets the trough of the other wave and there is no motion. The 4 antinodes are the points where there is maximum amplitude
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39. Base your answer to this questions 39, 40, 41 on the information and diagram below. A longitudinal wave moves to the right through a uniform medium, as shown below. Points A, B, C, D, and E represent the positions of particles of the medium.
The energy of this wave is related to its
1. amplitude
The energy of a longitudinal wave can be seen in the separation of particles in the compressions and rarefactions.
Reason 2. period
The amplitude of a wave is related to the wave’s energy. The energy or amplitude of a longitudinal wave can be seen in the degree of separation of particles in the compressions and rarefactions. In a longitudinal wave such as sound, as the amplitude increases, the sound becomes louder.
3. speed
4. wavelength
40. The wavelength of this wave is equal to the distance between points
1. A and B 2. A and C 3. B and C
4. B and E
A wavelength is the distance between two points that are in phase and have the same displacement.
Reason The wavelength in this longitudinal wave can be measured from point A to point C because these points are in phase, have the same displacement, and show one wave cycle of rarefaction and compression.
41. Which diagram best represents the motion of the particle at position C as the wave moves to the right?
Sound waves are longitudinal waves.
Reason In a longitudinal wave, the particles vibrate back and forth in the direction that the wave is traveling, as in choice 4.
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43. Which type of wave requires a material medium through which to travel?
1. radio wave
2. microwave
3. light wave
4. mechanical wave
45. A periodic wave having a frequency of 5.0 hertz and a speed of 10. meters per second has a wavelength of
1. 0.50 m
2. 2.0 m
3. 5.0 m
4. 50. m
46. The product of a wave’s frequency and its period is
1. one
2. its velocity
3. its wavelength
4. Planck’s constant
47. Two waves having the same frequency and amplitude are traveling in the same medium. Maximum constructive interference occurs at points where the phase difference between the two superposed waves is
1. 0°
The interference is constructive.
2. 90°
Reason 3. 180°
The maximum constructive interference will occur when the two waves are in phase, 0°, and are superimposed on one another. This will cause a crest to meet a crest and a trough to meet a trough.
4. 270°
49. Parallel wave fronts incident on an opening in a barrier are diffracted. For which combination of wavelength and size of opening will diffraction effects be greatest?
1. short wavelength and narrow opening
2. short wavelength and wide opening
3. long wavelength and narrow opening
Diffraction is the spreading of a wave front behind an obstruction or through an opening. Diffraction effects will be the greatest when the opening is narrow and the wavelength is long.
4. long wavelength and wide opening
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Hint Are the rays being “bent”? Reason This diagram illustrates refraction, which is the boundary phenomenon that occurs when a ray of light passes the boundary between areas of different optical density.
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