AP Physics 2: Algebra-Based Unit 6: Waves, Sound, and Physical Optics Practice Exam

Assessment for Unit 6: Waves, Sound, and Physical Optics

Estimated Time: 60 minutes

Exam Details

Questions: 52 total (52 multiple choice)
Time: 60 minutes (recommended)
Topics Covered: Unit 6: Waves, Sound, and Physical Optics
Format: Multiple Choice questions matching real exam difficulty
Scoring: Instant results with detailed explanations

A. Multiple-Choice Questions (52 Questions)

Select the one best answer for each question.

1. [Skill: 1.A | Topic: 6.1] Astronomers observe a supernova explosion in a distant galaxy. They are able to detect the visible light emitted by the event using space-based telescopes, but no sound from the explosion is ever detected on Earth, even by sensitive instruments. Which of the following statements best explains this observation? (A) The energy of the sound waves is converted into electromagnetic radiation before reaching Earth. (B) Sound waves are mechanical waves that require a medium to propagate, whereas light waves are electromagnetic waves that do not. (C) The wavelength of the sound waves is too large to be detected by instruments designed for electromagnetic radiation. (D) Sound waves transfer matter across the vacuum of space, which causes them to lose speed and dissipate before reaching Earth.

(A)The energy of the sound waves is converted into electromagnetic radiation before reaching Earth.(B)Sound waves are mechanical waves that require a medium to propagate, whereas light waves are electromagnetic waves that do not.(C)The wavelength of the sound waves is too large to be detected by instruments designed for electromagnetic radiation.(D)Sound waves transfer matter across the vacuum of space, which causes them to lose speed and dissipate before reaching Earth.

2. [Skill: 1.B | Topic: 6.1] A single transverse wave pulse is sent traveling to the right along a very long, horizontal string. A small piece of blue tape is attached to the string at position $x = L$. Which of the following describes the motion of the blue tape as the pulse passes through $x = L$? (A) The tape moves to the right with the pulse and remains at a new equilibrium position further down the string. (B) The tape moves only in a direction perpendicular to the string's length and returns to its original position. (C) The tape moves in a small clockwise circle, returning to its original position after the pulse passes. (D) The tape remains stationary because waves only transfer energy and not the physical particles of the medium.

(A)The tape moves to the right with the pulse and remains at a new equilibrium position further down the string.(B)The tape moves only in a direction perpendicular to the string's length and returns to its original position.(C)The tape moves in a small clockwise circle, returning to its original position after the pulse passes.(D)The tape remains stationary because waves only transfer energy and not the physical particles of the medium.

3. [Skill: 1.C | Topic: 6.1] A student performs an experiment with a long spring stretched to a constant tension. The student generates a wave pulse and measures its propagation speed $v$. If the student then increases the tension in the spring and generates a second pulse with a larger amplitude, how will the speed of the second pulse compare to the first? (A) The speed will be greater than $v$ because the speed of a mechanical wave depends on the properties of the medium. (B) The speed will be greater than $v$ because the larger amplitude carries more energy, which increases the propagation speed. (C) The speed will remain equal to $v$ because the speed of a wave pulse is independent of the tension in the medium. (D) The speed will be less than $v$ because the increased amplitude causes more internal friction within the spring.

(A)The speed will be greater than $v$ because the speed of a mechanical wave depends on the properties of the medium.(B)The speed will be greater than $v$ because the larger amplitude carries more energy, which increases the propagation speed.(C)The speed will remain equal to $v$ because the speed of a wave pulse is independent of the tension in the medium.(D)The speed will be less than $v$ because the increased amplitude causes more internal friction within the spring.

4. [Skill: 2.2 | Topic: 6.2] A mechanical oscillator is used to create periodic transverse waves on a long rope held under constant tension. Initially, the oscillator operates at a frequency $f_0$, producing waves with a wavelength $\lambda_0$. If the student adjusts the oscillator to vibrate at a new frequency of $2f_0$, which of the following correctly describes the new wavelength of the waves on the rope?

(A)The new wavelength is $2\lambda_0$ because wavelength is directly proportional to frequency.(B)The new wavelength is $\lambda_0$ because the wavelength depends only on the properties of the medium.(C)The new wavelength is $\lambda_0/2$ because the wave speed remains constant in the same medium.(D)The new wavelength is $\lambda_0/4$ because wave speed is proportional to the square of the frequency.

5. [Skill: 1.4 | Topic: 6.2] A periodic wave is traveling through a uniform medium. Which of the following statements correctly relates the temporal and spatial properties of the wave?

(A)The period $T$ is the distance between two consecutive crests, while the wavelength $\lambda$ is the time it takes for one full cycle.(B)The frequency $f$ is the number of cycles per unit time, and it is the reciprocal of the period $T$.(C)Increasing the amplitude of the wave will necessarily increase the frequency of the wave.(D)The wavelength $\lambda$ can be determined solely by measuring the time interval between two pulses passing a fixed point.

6. [Skill: 5.1 | Topic: 6.2] A physics student is analyzing a longitudinal sound wave traveling through a column of air. The student measures the distance between the center of a compression (region of high pressure) and the center of the immediately adjacent rarefaction (region of low pressure) to be $0.25$ m. If the frequency of the sound source is $680$ Hz, what is the speed of sound in the air column?

(A)170 m/s(B)272 m/s(C)340 m/s(D)680 m/s

7. [Skill: 1.4 | Topic: 6.3] A monochromatic light wave with frequency $f_0$ and wavelength $\lambda_0$ in air travels into a block of glass with an index of refraction $n = 1.5$. Which of the following correctly describes the frequency $f_{glass}$ and the wavelength $\lambda_{glass}$ of the light while it is inside the glass?

(A)$f_{glass} = f_0$ and $\lambda_{glass} = \lambda_0$(B)$f_{glass} = f_0$ and $\lambda_{glass} = \frac{\lambda_0}{1.5}$(C)$f_{glass} = 1.5 f_0$ and $\lambda_{glass} = \lambda_0$(D)$f_{glass} = \frac{f_0}{1.5}$ and $\lambda_{glass} = \frac{\lambda_0}{1.5}$

8. [Skill: 6.4 | Topic: 6.3] A student is conducting an experiment to distinguish between different types of waves. The student has two sources: Source A produces a sound wave in air, and Source B produces a light wave in a vacuum. Both waves are directed toward a polarizing filter. Which of the following correctly predicts and justifies the observations?

(A)Both waves will be polarized because all waves can oscillate in a single plane when passing through a boundary.(B)Neither wave will be polarized because polarization only occurs when waves reflect off a surface, not when they pass through a filter.(C)Only the light wave will be polarized because it is a transverse wave, whereas the sound wave is longitudinal and cannot be polarized.(D)Only the sound wave will be polarized because longitudinal waves oscillate parallel to the direction of travel, allowing them to align with the filter.

9. [Skill: 2.2 | Topic: 6.3] A periodic wave travels along a light string that is connected to a much heavier, denser string. The wave speed in the light string is $v_1 = 20 \text{ m/s}$ and the wavelength is $\lambda_1 = 0.5 \text{ m}$. In the heavier string, the wave speed is $v_2 = 10 \text{ m/s}$. What is the wavelength $\lambda_2$ of the wave after it has been transmitted into the heavier string?

(A)0.25 m(B)0.5 m(C)1.0 m(D)2.0 m

10. [Skill: 1.1 | Topic: 6.3] An unpolarized beam of light is incident upon a boundary between air and a transparent material. A portion of the light is reflected and a portion is transmitted. Which of the following is a true statement regarding the properties of the wave at this boundary?

(A)The transmitted wave will have a higher frequency if the material is denser than air.(B)The reflected wave will always be completely polarized regardless of the angle of incidence.(C)The frequency of the transmitted wave is identical to the frequency of the incident wave.(D)The wavelength of the transmitted wave will be longer than the wavelength of the incident wave if the speed of light in the material is slower than in air.

11. [Skill: 1.1 | Topic: 6.4] An electromagnetic wave is propagating through a vacuum in the positive $x$-direction. At a particular instant in time and at a specific location, the electric field vector $\vec{E}$ is oscillating in the positive $y$-direction. Which of the following correctly describes the direction of the magnetic field vector $\vec{B}$ at that same instant and the classification of this wave?

(A)The magnetic field points in the positive $z$-direction; the wave is transverse.(B)The magnetic field points in the negative $z$-direction; the wave is longitudinal.(C)The magnetic field points in the positive $y$-direction; the wave is transverse.(D)The magnetic field points in the negative $x$-direction; the wave is longitudinal.

12. [Skill: 6.4 | Topic: 6.4] Which of the following statements best justifies why electromagnetic waves, such as light from distant galaxies, can travel through the vacuum of space to reach Earth, whereas sound waves cannot?

(A)Electromagnetic waves have much higher frequencies than sound waves, allowing them to penetrate the vacuum.(B)Electromagnetic waves are self-propagating through the interaction of oscillating electric and magnetic fields and do not require a material medium.(C)The vacuum of space contains a thin distribution of atoms that act as a medium for transverse waves but not for longitudinal waves.(D)Electromagnetic waves possess mass in the form of photons, which allows them to travel via inertia through empty space.

13. [Skill: 2.2 | Topic: 6.4] A student is comparing three different regions of the electromagnetic spectrum: Ultraviolet (UV) radiation, Microwaves, and X-rays. Which of the following correctly ranks these waves in order of increasing wavelength and correctly compares their speeds in a vacuum?

(A)Wavelength: Microwaves < UV < X-rays; Speed: X-rays travel the fastest.(B)Wavelength: X-rays < UV < Microwaves; Speed: All three travel at the same speed $c$.(C)Wavelength: UV < X-rays < Microwaves; Speed: All three travel at the same speed $c$.(D)Wavelength: X-rays < UV < Microwaves; Speed: Microwaves travel the slowest because they have the lowest energy.

14. [Skill: 1.1 | Topic: 6.5] An ambulance travels at a constant speed $v_s$ toward a stationary observer while emitting a sound wave of constant frequency $f_0$. Which of the following best describes the physical spacing of the wavefronts in the region between the ambulance and the observer, and the resulting frequency $f_{obs}$ measured by the observer?

(A)The wavefronts are closer together than if the source were stationary, and $f_{obs} > f_0$.(B)The wavefronts are further apart than if the source were stationary, and $f_{obs} < f_0$.(C)The wavefronts are closer together than if the source were stationary, and $f_{obs} < f_0$.(D)The wavefronts are further apart than if the source were stationary, and $f_{obs} > f_0$. Gold

15. [Skill: 5.1 | Topic: 6.5] A stationary student is observing two identical police cars, Car X and Car Y, which are both sounding their sirens at a rest frequency of $f_0$. Car X is moving directly toward the student at a speed of $15\text{ m/s}$. Car Y is moving directly toward the student at a speed of $30\text{ m/s}$. If $f_X$ is the frequency the student hears from Car X and $f_Y$ is the frequency the student hears from Car Y, which of the following correctly ranks the frequencies?

(A)$f_0 > f_X > f_Y$(B)$f_Y > f_X > f_0$(C)$f_X = f_Y > f_0$(D)$f_Y > f_0 > f_X$

16. [Skill: 1.1 | Topic: 6.6] Two transverse wave pulses, Pulse 1 and Pulse 2, travel toward each other along a horizontal string. Pulse 1 has a maximum displacement of $+4.0\text{ cm}$ and is moving to the right. Pulse 2 has a maximum displacement of $-2.5\text{ cm}$ and is moving to the left. At the instant the centers of the two pulses coincide, what is the net displacement of the string at that location?

(A)$+6.5\text{ cm}$(B)$+4.0\text{ cm}$(C)$+1.5\text{ cm}$(D)$-1.5\text{ cm}$

17. [Skill: 1.4 | Topic: 6.6] A string of length $L$ is fixed at both ends and vibrates at its fundamental frequency, forming a standing wave. Which of the following correctly identifies the wavelength $\lambda$ of this standing wave and the number of nodes present on the string?

(A)$\lambda = L$ and there are 2 nodes.(B)$\lambda = 2L$ and there are 2 nodes.(C)$\lambda = 2L$ and there are 3 nodes.(D)$\lambda = 0.5L$ and there is 1 node.

18. [Skill: 6.4 | Topic: 6.6] A student uses a mechanical vibrator to create a standing wave on a string that is attached to a wall. The student observes several points on the string that appear to remain stationary despite the continuous vibration of the source. Which of the following best explains the physical cause of these stationary points?

(A)The points are locations where only the reflected wave from the wall has zero amplitude.(B)The points are locations where the incident wave and the reflected wave are always in phase, resulting in constructive interference.(C)The points are locations where the incident wave and the reflected wave are always $180^{\circ}$ out of phase, resulting in destructive interference.(D)The points are locations where the string's tension is so high that the transverse displacement is prevented.

19. [Skill: 1.1 | Topic: 6.7] A beam of monochromatic light is directed toward a single narrow slit of width $w$. A viewing screen is placed at a large distance from the slit. If light behaved strictly as a stream of particles traveling in straight lines, which of the following best describes the predicted observation on the screen compared to the actual observed wave behavior?

(A)Particle Prediction: A single bright area on the screen with the same width as the slit. Actual Observation: A central bright fringe that is much wider than the slit, flanked by alternating dark and bright fringes.(B)Particle Prediction: A series of alternating bright and dark fringes. Actual Observation: A single bright area on the screen with the same width as the slit.(C)Particle Prediction: No light would reach the screen because the slit is too narrow. Actual Observation: A uniform illumination of the entire screen.(D)Particle Prediction: A single bright area on the screen with the same width as the slit. Actual Observation: The light would be reflected back toward the source, leaving the screen dark.

20. [Skill: 1.4 | Topic: 6.7] In a ripple tank experiment, water waves with wavelength $\lambda$ approach a barrier with a single opening of width $w$. A student wants to modify the setup to make the diffraction (spreading) of the waves as pronounced as possible. Which of the following changes would achieve this goal?

(A)Increase the width of the opening $w$ while keeping the wavelength $\lambda$ constant.(B)Decrease the wavelength $\lambda$ while keeping the width of the opening $w$ constant.(C)Decrease the width of the opening $w$ until it is comparable to the wavelength $\lambda$.(D)Increase the frequency of the wave source while keeping the width of the opening $w$ constant.

21. [Skill: 6.4 | Topic: 6.7] A student stands in a hallway and can hear a teacher speaking inside a classroom through an open doorway, even though the student cannot see the teacher. Which of the following claims correctly explains this phenomenon using the properties of waves?

(A)Sound waves are longitudinal, allowing them to pass through solid walls, whereas light waves are transverse and are blocked.(B)The wavelength of the sound waves is comparable to the width of the doorway, causing significant diffraction, while the wavelength of light is much smaller than the doorway.(C)The doorway acts as a refractive medium that bends the sound waves toward the student but does not affect the light waves.(D)The speed of sound is much slower than the speed of light, which allows sound waves more time to spread out around the corner.

22. [Skill: 1.1 | Topic: 6.8] A beam of monochromatic light is directed at a barrier containing two narrow, parallel slits. On a distant screen, a pattern of alternating bright and dark fringes is observed. Which of the following statements best explains how this experiment provides evidence for the wave nature of light? (A) The light particles collide with the edges of the slits and scatter in a predictable geometric pattern. (B) Light waves from the two slits overlap and combine through the principle of superposition, creating constructive and destructive interference. (C) The bright fringes represent regions where light particles are most concentrated after being refracted by the slit openings. (D) The pattern is caused by the light waves changing their frequency as they pass through the narrow openings of the slits.

(A)The light particles collide with the edges of the slits and scatter in a predictable geometric pattern.(B)Light waves from the two slits overlap and combine through the principle of superposition, creating constructive and destructive interference.(C)The bright fringes represent regions where light particles are most concentrated after being refracted by the slit openings.(D)The pattern is caused by the light waves changing their frequency as they pass through the narrow openings of the slits.

23. [Skill: 1.4 | Topic: 6.8] A student performs an experiment using a double-slit apparatus and observes a pattern of bright fringes on a screen. The student then replaces the double-slit mask with a diffraction grating that has the same slit separation $d$ as the original double-slit mask. Which of the following correctly describes the change in the interference pattern observed on the screen? (A) The bright fringes will appear at the same locations but will be significantly narrower and more intense. (B) The bright fringes will be spaced much closer together because the number of slits has increased. (C) The pattern will disappear and be replaced by a single, wide central maximum due to increased diffraction. (D) The bright fringes will become wider and less distinct because of the superposition of multiple wave sources.

(A)The bright fringes will appear at the same locations but will be significantly narrower and more intense.(B)The bright fringes will be spaced much closer together because the number of slits has increased.(C)The pattern will disappear and be replaced by a single, wide central maximum due to increased diffraction.(D)The bright fringes will become wider and less distinct because of the superposition of multiple wave sources.

24. [Skill: 1.C | Topic: 6.9] A beam of monochromatic light in air ($n_{air} = 1.00$) is incident nearly perpendicular to a thin layer of oil ($n_{oil} = 1.45$) floating on water ($n_{water} = 1.33$). Which of the following correctly describes the phase changes that occur for the light reflected from the top surface of the oil and the light reflected from the oil-water interface?

(A)There is a $180^{\circ}$ phase change at the top surface and a $180^{\circ}$ phase change at the oil-water interface.(B)There is a $180^{\circ}$ phase change at the top surface and no phase change at the oil-water interface.(C)There is no phase change at the top surface and a $180^{\circ}$ phase change at the oil-water interface.(D)There is no phase change at either the top surface or the oil-water interface.

25. [Skill: 1.D | Topic: 6.9] A camera lens ($n_{glass} = 1.60$) is coated with a thin layer of magnesium fluoride ($n_{film} = 1.38$) to minimize reflections of blue light ($\lambda = 414$ nm in air). How does this coating function to reduce the intensity of reflected light?

(A)The coating increases the speed of light, causing the reflected waves to become out of phase with the incident waves.(B)The reflected waves from the top and bottom surfaces of the coating undergo identical phase shifts upon reflection, so a path length difference of $\lambda_{film}/2$ causes destructive interference.(C)The coating absorbs the specific wavelength of blue light, preventing it from reflecting back to the observer.(D)The reflected waves from the top and bottom surfaces undergo different phase shifts, so a path length difference of $\lambda_{film}$ is required to create destructive interference.

26. [Skill: 1.4 | Topic: 6.1] A student attaches one end of a long, horizontal string to a wall and holds the other end. The student quickly moves their hand up and down once, creating a single wave pulse that travels toward the wall. A small piece of blue tape is attached to the middle of the string. Which of the following best describes the motion of the blue tape and the transfer of energy as the pulse passes the tape?

(A)The tape moves toward the wall with the pulse, and energy is transferred toward the wall.(B)The tape moves up and then back down to its equilibrium position, and energy is transferred toward the wall.(C)The tape moves up and then back down to its equilibrium position, but no energy is transferred because it is a single pulse.(D)The tape moves toward the wall with the pulse, but no matter is transferred, so no energy is transferred.

Refer to the figure below.

27. [Skill: 6.4 | Topic: 6.1] A specialized alarm clock is placed inside a sealed glass vacuum chamber. The clock is set to ring a bell while simultaneously flashing a bright LED light. A student observes the chamber from the outside after all the air has been evacuated. Which of the following correctly predicts what the student will observe and provides the correct reasoning?

(A)The student will see the light and hear the bell because both are electromagnetic disturbances.(B)The student will neither see the light nor hear the bell because waves require a medium to propagate.(C)The student will see the light but will not hear the bell because light is an electromagnetic wave that does not require a medium, while sound is a mechanical wave that does.(D)The student will hear the bell but will not see the light because sound can travel through the glass walls while light is reflected by the vacuum.

28. [Skill: 2.2 | Topic: 6.1] A wave pulse is generated on a string with a linear mass density of $\mu$. The pulse travels at a speed $v$. If the string is replaced with a new string made of the same material but with a larger diameter, such that the linear mass density becomes $4\mu$, while the tension in the string remains constant, what is the new speed of a wave pulse generated on this string?

(A)$4v$(B)$2v$(C)$v/2$(D)$v/4$

29. [Skill: 5.1 | Topic: 6.1] Two different wave pulses, Pulse 1 and Pulse 2, are sent down the same uniform horizontal spring. Pulse 1 has a maximum vertical displacement (amplitude) of $0.10\text{ m}$, and Pulse 2 has a maximum vertical displacement of $0.20\text{ m}$. Which of the following is a correct comparison of the speed and energy of the two pulses?

(A)Pulse 2 travels faster than Pulse 1 because it has a larger amplitude.(B)Pulse 2 travels at the same speed as Pulse 1, but Pulse 2 carries more energy.(C)Pulse 2 travels slower than Pulse 1 because it moves a greater mass of the spring upward.(D)Pulse 2 and Pulse 1 travel at the same speed and carry the same amount of energy because they are in the same medium.

Refer to the figure below.

30. [Skill: 1.1 | Topic: 6.2] A transverse periodic wave travels along a string. The graph below shows the displacement of the string as a function of position at a specific instant in time. If the frequency of the wave is 10 Hz, what is the speed of the wave?

(A)2.5 m/s(B)5.0 m/s(C)10 m/s(D)20 m/s

31. [Skill: 2.2 | Topic: 6.2] A student uses a mechanical oscillator to create periodic waves on a stretched horizontal spring. The speed of the wave depends only on the tension and linear mass density of the spring. If the student adjusts the oscillator to double the frequency of the waves while keeping the tension in the spring constant, which of the following describes the change in the wavelength?

(A)The wavelength doubles because wavelength is directly proportional to frequency.(B)The wavelength remains the same because it only depends on the properties of the medium.(C)The wavelength is reduced to one-half of its original value.(D)The wavelength is reduced to one-fourth of its original value.

32. [Skill: 6.4 | Topic: 6.3] A beam of monochromatic light travels through vacuum and enters a transparent glass slab with an index of refraction $n = 1.5$. Which of the following correctly describes the change in the light wave's frequency $f$ and speed $v$ as it moves from the vacuum into the glass? (A) $f$ stays the same; $v$ increases. (B) $f$ stays the same; $v$ decreases. (C) $f$ increases; $v$ stays the same. (D) $f$ decreases; $v$ decreases.

(A)$f$ stays the same; $v$ increases.(B)$f$ stays the same; $v$ decreases.(C)$f$ increases; $v$ stays the same.(D)$f$ decreases; $v$ decreases.

33. [Skill: 1.4 | Topic: 6.3] A student is characterizing three different types of waves generated in a laboratory setting: Wave 1: A sound wave traveling through a nitrogen-filled tube. Wave 2: A light wave traveling through a fiber optic cable. Wave 3: A wave on a long slinky where the coils oscillate back and forth parallel to the direction of wave propagation. The student attempts to pass each wave through a device designed to polarize transverse waves. Which of the following waves can be polarized? (A) Wave 2 only (B) Wave 1 and Wave 2 only (C) Wave 2 and Wave 3 only (D) Wave 1, Wave 2, and Wave 3

(A)Wave 2 only(B)Wave 1 and Wave 2 only(C)Wave 2 and Wave 3 only(D)Wave 1, Wave 2, and Wave 3

Refer to the figure below.

34. [Skill: 1.1 | Topic: 6.3] [Image Cue]: A diagram shows a string consisting of two segments joined at a boundary. Segment 1 is a light string with low linear mass density, and Segment 2 is a heavy string with high linear mass density. A single pulse is shown in Segment 1 moving toward the boundary. A wave pulse travels along Segment 1 toward the boundary with Segment 2. The wave speed in Segment 1 is $v_1$ and the wave speed in Segment 2 is $v_2$, where $v_1 > v_2$. Which of the following best describes the behavior of the wave at the boundary? (A) The wave is entirely reflected back into Segment 1 with no transmission. (B) The wave is entirely transmitted into Segment 2 with no reflection. (C) A portion of the wave is transmitted into Segment 2 with a smaller wavelength than in Segment 1. (D) A portion of the wave is transmitted into Segment 2 with a higher frequency than in Segment 1.

(A)The wave is entirely reflected back into Segment 1 with no transmission.(B)The wave is entirely transmitted into Segment 2 with no reflection.(C)A portion of the wave is transmitted into Segment 2 with a smaller wavelength than in Segment 1.(D)A portion of the wave is transmitted into Segment 2 with a higher frequency than in Segment 1.

35. [Skill: 2.2 | Topic: 6.3] Unpolarized light of intensity $I_0$ is incident on a linear polarizer. The light that emerges from this first polarizer then strikes a second linear polarizer whose transmission axis is oriented at an angle of $90^{\circ}$ relative to the first. Which of the following correctly identifies the state of the light after the first polarizer and the intensity after the second polarizer? (A) After 1st: Polarized; Intensity after 2nd: $\frac{1}{2} I_0$ (B) After 1st: Unpolarized; Intensity after 2nd: $0$ (C) After 1st: Polarized; Intensity after 2nd: $0$ (D) After 1st: Polarized; Intensity after 2nd: $I_0$

(A)After 1st: Polarized; Intensity after 2nd: $\frac{1}{2} I_0$(B)After 1st: Unpolarized; Intensity after 2nd: $0$(C)After 1st: Polarized; Intensity after 2nd: $0$(D)After 1st: Polarized; Intensity after 2nd: $I_0$

36. [Skill: 1.1 | Topic: 6.4] A plane electromagnetic wave is propagating through a vacuum in the $+z$ direction. At a particular instant in time, the electric field vector $\vec{E}$ at a specific point in space is oriented along the $+y$ axis. Which of the following best describes the orientation of the magnetic field vector $\vec{B}$ at that same point and instant?

(A)The magnetic field vector points in the $+x$ direction.(B)The magnetic field vector points in the $-x$ direction.(C)The magnetic field vector points in the $+y$ direction.(D)The magnetic field vector points in the $-z$ direction.

37. [Skill: 6.4 | Topic: 6.4] A spacecraft in the deep vacuum of interstellar space, far from any planetary atmosphere, sends a radio signal and a high-intensity laser pulse (visible light) back to a receiving station on Earth. Which of the following statements correctly compares these two signals as they travel through the vacuum?

(A)The laser pulse will reach Earth, but the radio signal will not because radio waves require a gaseous medium to propagate.(B)Both signals will travel at the same speed $c$ because all electromagnetic waves can propagate through a vacuum without a medium.(C)The radio signal will travel faster than the laser pulse because it has a longer wavelength.(D)The laser pulse will travel faster than the radio signal because its higher frequency allows it to perturb the vacuum more efficiently.

38. [Skill: 1.1 | Topic: 6.5] A stationary student stands on a sidewalk as an ambulance with a siren emitting a sound of constant rest frequency $f_0$ approaches at a constant speed $v_s$. Which of the following best describes the physical spacing of the wavefronts in front of the ambulance and the frequency $f_{obs}$ detected by the student?

(A)The wavefronts are compressed (closer together) relative to a stationary source, and $f_{obs} > f_0$.(B)The wavefronts are compressed (closer together) relative to a stationary source, and $f_{obs} < f_0$.(C)The wavefronts are elongated (farther apart) relative to a stationary source, and $f_{obs} > f_0$.(D)The wavefronts are elongated (farther apart) relative to a stationary source, and $f_{obs} < f_0$.

39. [Skill: 2.2 | Topic: 6.5] Two identical sound sources, $S_1$ and $S_2$, both emit sound waves with a rest frequency of $440\text{ Hz}$. Source $S_1$ moves toward a stationary observer at a constant speed of $20\text{ m/s}$. Source $S_2$ moves toward the same stationary observer at a constant speed of $40\text{ m/s}$. If $f_1$ and $f_2$ are the frequencies measured by the observer for $S_1$ and $S_2$ respectively, which of the following correctly ranks the frequencies?

(A)$f_1 = f_2 = 440\text{ Hz}$(B)$f_2 > f_1 > 440\text{ Hz}$(C)$f_1 > f_2 > 440\text{ Hz}$(D)$440\text{ Hz} > f_2 > f_1$

Refer to the figure below.

40. [Skill: 5.1 | Topic: 6.5] [Image Cue]: Line graph, 'Observed Frequency vs. Time', Vertical axis labeled $f_{obs}$, horizontal axis labeled $t$. The graph shows a high, constant horizontal line from $t = 0$ to $t = t_1$, a vertical drop at $t = t_1$, and a lower, constant horizontal line from $t = t_1$ to $t = t_2$. A stationary microphone records the frequency of a sound source that is moving along a straight line at a constant speed. The source passes directly by the microphone at time $t_1$. Which of the following statements best justifies the behavior shown in the graph?

(A)The frequency is higher before $t_1$ because the source is moving toward the microphone, and lower after $t_1$ because it is moving away.(B)The frequency is higher before $t_1$ because the sound waves travel faster when the source moves toward the microphone.(C)The frequency is constant before $t_1$ because the source is accelerating toward the microphone at a constant rate.(D)The frequency drops at $t_1$ because the source stops emitting sound for a brief moment as it passes the microphone.

Refer to the figure below.

41. **1.** [Skill: 1.B | Topic: 6.6] Two rectangular wave pulses, $P$ and $Q$, travel toward each other on a horizontal string as shown in the diagram. Pulse $P$ has an amplitude of $+4.0$ cm and a width of $2.0$ cm. Pulse $Q$ has an amplitude of $-2.5$ cm and a width of $2.0$ cm. When the two pulses completely overlap at time $t$, what is the resulting displacement of the string in the region of overlap? (A) $+6.5$ cm (B) $+1.5$ cm (C) $-1.5$ cm (D) $0.0$ cm

(A)+6.5 cm(B)+1.5 cm(C)-1.5 cm(D)0.0 cm

42. **2.** [Skill: 2.B | Topic: 6.6] A string of length $L$ is stretched and fixed at both ends. A student uses a mechanical vibrator to create a standing wave pattern on the string. The student observes that there are exactly three antinodes present between the fixed ends. Which of the following represents the wavelength $\lambda$ of the component waves that produce this standing wave? (A) $\lambda = \frac{L}{3}$ (B) $\lambda = \frac{2L}{3}$ (C) $\lambda = L$ (D) $\lambda = \frac{3L}{2}$

(A)$\lambda $= L/3(B)$\lambda $= 2L/3(C)$\lambda $= L(D)$\lambda $= 3L/2

43. **3.** [Skill: 1.B | Topic: 6.6] A hollow pipe of length $L$ is open at one end and closed at the other. A standing wave is established in the pipe at its fundamental frequency $f_1$. If the pipe is replaced with a new pipe of the same type (one end open, one end closed) but with a length of $0.5L$, how does the new fundamental frequency $f_{new}$ compare to the original frequency $f_1$? (A) $f_{new} = \frac{1}{4}f_1$ (B) $f_{new} = \frac{1}{2}f_1$ (C) $f_{new} = 2f_1$ (D) $f_{new} = 4f_1$

(A)f_{new} = 1/4 f_1(B)f_{new} = 1/2 f_1(C)f_{new} = 2f_1(D)f_{new} = 4f_1

Refer to the figure below.

44. [Skill: 1.1 | Topic: 6.7] A series of planar water waves with wavelength $\lambda$ are generated in a ripple tank and travel toward a barrier with a single opening of width $w$. The wave patterns are observed on the opposite side of the barrier. In which of the following scenarios will the waves exhibit the most significant spreading (diffraction) into the region behind the barrier?

(A)When the width $w$ is much greater than the wavelength $\lambda$.(B)When the width $w$ is approximately equal to or smaller than the wavelength $\lambda$.(C)When the amplitude of the incident waves is doubled while keeping $w$ and $\lambda$ constant.(D)When the frequency of the waves is increased while keeping the wave speed and $w$ constant.

45. [Skill: 6.4 | Topic: 6.7] A student stands in a hallway and can hear a conversation occurring inside a room with an open door, even though the student cannot see the people talking. Which of the following best justifies why the sound waves 'bend' around the doorframe while the light waves do not appear to do so?

(A)Sound waves are longitudinal and light waves are transverse, and only longitudinal waves can diffract around large obstacles.(B)The speed of sound is much slower than the speed of light, and slower waves experience more diffraction.(C)The wavelength of audible sound is comparable to the width of the door, whereas the wavelength of visible light is many orders of magnitude smaller than the door.(D)Sound waves require a medium to travel, and the air in the hallway acts as a waveguide to pull the sound around the corner.

46. [Skill: 7.2 | Topic: 6.7] Monochromatic light of wavelength $\lambda$ passes through a single narrow slit of width $a$ and forms a diffraction pattern on a screen located a distance $L$ away. If the experiment is repeated using a different setup, which of the following changes would result in a diffraction pattern where the central maximum is wider (more spread out)?

(A)Replacing the light source with one that has a higher frequency.(B)Increasing the width of the slit $a$.(C)Decreasing the width of the slit $a$.(D)Moving the screen closer to the slit (decreasing $L$).

47. [Skill: 6.4 | Topic: 6.8] A beam of monochromatic light is incident on a barrier containing two extremely narrow, parallel slits separated by a distance $d$. A screen is placed a distance $L$ away from the barrier, where $L gg d$. An interference pattern consisting of alternating bright and dark fringes is observed. Which of the following best explains why this experiment provides evidence for the wave nature of light rather than the particle nature of light?

(A)Light particles would be expected to travel in straight lines through the slits, producing only two bright spots on the screen directly behind the openings.(B)The bright fringes are caused by light particles colliding with each other and increasing their kinetic energy before hitting the screen.(C)The dark fringes are caused by light particles being absorbed by the air molecules between the barrier and the screen.(D)The pattern of fringes only appears when the intensity of the light is high enough for particles to stack on top of one another.

48. [Skill: 1.4 | Topic: 6.8] A student performs a double-slit interference experiment using a laser of wavelength $\lambda$ and a slide with two slits separated by distance $d$. The student then replaces the double-slit slide with a diffraction grating that has many more slits, but the distance between adjacent slits remains $d$. Which of the following correctly describes the change in the interference pattern observed on the screen?

(A)The positions of the principal maxima will shift closer to the center of the screen, and the fringes will become wider.(B)The positions of the principal maxima will remain at the same locations, but the maxima will become narrower and brighter.(C)The dark fringes will disappear, resulting in a continuous band of light across the screen.(D)The interference pattern will be replaced by a single, broad diffraction envelope with no distinct fringes.

Refer to the figure below.

49. [Skill: 2.2 | Topic: 6.8] In a double-slit experiment, light of wavelength $\lambda$ passes through two slits separated by distance $d$. At a particular point $P$ on a distant screen, the second-order bright fringe ($m = 2$) is observed. What is the difference in the path lengths traveled by the light from each of the two slits to point $P$?

(A)$\frac{1}{2}\lambda$(B)$\lambda$(C)$2\lambda$(D)$\frac{d}{2}$

50. [Skill: 1.4 | Topic: 6.9] Monochromatic light with wavelength $\lambda$ in air is incident normally on a thin layer of oil ($n_{oil} = 1.45$) floating on water ($n_{water} = 1.33$). Which of the following correctly describes the phase changes that occur when the light reflects off the top surface of the oil and the bottom surface of the oil?

(A)There is a $180^\circ$ phase change at the air-oil interface and no phase change at the oil-water interface.(B)There is no phase change at the air-oil interface and a $180^\circ$ phase change at the oil-water interface.(C)There are $180^\circ$ phase changes at both the air-oil and the oil-water interfaces.(D)There are no phase changes at either the air-oil or the oil-water interfaces.

51. [Skill: 2.2 | Topic: 6.9] A glass camera lens ($n_{glass} = 1.60$) is coated with a thin film of magnesium fluoride ($n_{film} = 1.38$) to minimize reflections of light with wavelength $\lambda$ in a vacuum. What is the minimum non-zero thickness $t$ of the coating that will produce the desired destructive interference?

(A)$\lambda / 2$(B)$\lambda / (2n_{film})$(C)$\lambda / 4$(D)$\lambda / (4n_{film})$

Refer to the figure below.

52. [Skill: 6.4 | Topic: 6.9] A vertical soap film ($n = 1.33$) is held in a wire frame. Due to gravity, the film is thinner at the top and thicker at the bottom, forming a wedge shape. When the film is illuminated with white light and viewed in reflection, the very top of the film appears black (dark) just before it becomes thin enough to break. Which of the following best explains this observation?

(A)At the top of the film, the thickness is much larger than the wavelength of light, causing all colors to interfere constructively.(B)The thickness of the film at the top is nearly zero, and the phase change at the first surface reflection causes the two reflected waves to be $180^\circ$ out of phase.(C)The index of refraction of the soap film is lower than that of the surrounding air, preventing any phase changes from occurring.(D)The light undergoes multiple internal reflections within the wedge, which averages the intensity of all wavelengths to zero.

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