Diffraction
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AP Physics 2 › Diffraction
A speaker emits a steady tone toward two hallways separated by a wall with an opening. Opening X is $0.20,\text{m}$ wide and opening Y is $1.0,\text{m}$ wide. The sound wavelength is about $0.34,\text{m}$. Which opening produces greater spreading into the hallway?
Opening Y, because a larger opening increases diffraction
Opening X, because its width is closer to the wavelength
Opening X, because sound travels faster through smaller openings
Opening Y, because more power passes through
Explanation
This question tests understanding of diffraction. Diffraction is the spreading of waves as they pass through openings, with more spreading occurring when the opening width is comparable to the wavelength. Opening X (0.20 m) is closer in size to the sound wavelength (0.34 m) with a ratio of 0.34/0.20 = 1.7, while opening Y (1.0 m) gives a ratio of 0.34/1.0 = 0.34. The smaller opening X produces greater diffraction because its width is more comparable to the wavelength. Choice A incorrectly assumes larger openings cause more diffraction, confusing total energy transmission with angular spreading. The key principle: diffraction is strongest when opening size matches wavelength.
A ripple tank produces waves of wavelength $\lambda$ that pass through a gap and then spread. The motor is adjusted to double the amplitude while keeping $\lambda$ and the gap width constant. Compared with before, the diffraction (angular spreading) is
smaller, because higher intensity reduces diffraction
unchanged, because diffraction depends on $\lambda$ relative to gap width
greater, because higher amplitude increases diffraction
greater, because the wave speed increases with amplitude
Explanation
This question tests understanding of diffraction. Diffraction is the spreading of waves after passing through an opening, and the angular spreading depends only on the ratio of wavelength to gap width, not on wave amplitude or intensity. Doubling the amplitude increases the energy and intensity of the waves but does not change the wavelength or gap width, so the diffraction angle remains unchanged. Choice A incorrectly assumes amplitude affects diffraction, but this confuses wave energy with the geometric spreading pattern. Remember: diffraction depends only on the wavelength-to-opening ratio, not on wave amplitude or intensity.
A tank produces circular water waves of wavelength $\lambda$ that encounter a small post. In trial 1 the post diameter is $0.5\lambda$; in trial 2 it is $3\lambda$. The wave speed is unchanged. In which trial will the waves bend around the post the most?
Trial 1, because the amplitude is larger near the post
Trial 2, because a larger obstacle increases wave intensity
Trial 1, because the obstacle size is smaller relative to $\lambda$
Trial 2, because a larger obstacle increases wave speed
Explanation
This question tests understanding of diffraction. Diffraction is the bending of waves around obstacles, with more bending occurring when the obstacle size is comparable to or smaller than the wavelength. In trial 1, the post diameter (0.5λ) is smaller than the wavelength, allowing waves to bend significantly around it. In trial 2, the post diameter (3λ) is much larger than the wavelength, causing minimal bending as waves are mostly blocked. Choice A incorrectly relates obstacle size to wave intensity, but diffraction depends on the size ratio, not intensity. The strategy is: smaller obstacles relative to wavelength produce more diffraction around them.
Microwaves of wavelength $3.0,\text{cm}$ pass through a square opening of side $6.0,\text{cm}$. In a second setup, radio waves of wavelength $30,\text{cm}$ pass through the same opening. Both have the same power. Which setup shows greater diffraction beyond the opening?
Radio waves, because $\lambda$ is larger compared with the opening
Microwaves, because they have higher intensity
Microwaves, because they travel faster in air
Radio waves, because their amplitude is larger
Explanation
This question tests understanding of diffraction. Diffraction is the spreading of waves after passing through an opening, with the amount of spreading determined by the ratio of wavelength to opening size. The radio waves (λ = 30 cm) have a ratio of 30/6 = 5, while the microwaves (λ = 3 cm) have a ratio of 3/6 = 0.5. Since the radio waves have a much larger wavelength relative to the opening, they experience greater diffraction. Choice C incorrectly suggests that wave speed varies between different electromagnetic waves in air, but all EM waves travel at speed c in air. Remember: larger wavelength relative to opening size means more diffraction.
Two waves approach identical narrow openings. Wave 1 has wavelength $2,\text{cm}$; wave 2 has wavelength $6,\text{cm}$. Both travel at the same speed in the medium. Which wave diffracts more after passing through the opening?
Wave 1, because it has greater intensity
Wave 2, because its wavelength is larger relative to the opening
Wave 2, because its speed is higher
Wave 1, because its frequency is higher
Explanation
This question tests understanding of diffraction. Diffraction is the spreading of waves after passing through an opening, with the amount of spreading determined by the ratio of wavelength to opening size. Wave 2 has a wavelength of 6 cm, which is three times larger than wave 1's wavelength of 2 cm. Since both pass through identical openings, wave 2 has a larger wavelength-to-opening ratio and therefore diffracts more. Choice A incorrectly relates frequency to diffraction, but higher frequency means shorter wavelength and less diffraction for a given opening. The key principle: for identical openings, longer wavelength produces more diffraction.
A monochromatic sound wave passes through a doorway into a hallway. The doorway width is fixed. Compared to a higher-frequency sound, a lower-frequency sound has a larger wavelength. Which sound shows the greatest diffraction (spreading) into the hallway?
The lower-frequency sound because its wavelength is larger relative to the doorway
The higher-frequency sound because it travels faster
The higher-frequency sound because its intensity is greater
The lower-frequency sound because its amplitude is larger
Explanation
This question tests understanding of diffraction. Diffraction occurs when waves bend around obstacles or spread out after passing through openings, with the amount of spreading determined by the ratio of wavelength to opening size. Lower frequency sounds have longer wavelengths (since v = fλ and v is constant in air), making their wavelength larger relative to the fixed doorway width. This larger λ/width ratio causes greater diffraction and more spreading into the hallway. Choice A incorrectly assumes wave speed depends on frequency, but all sound waves travel at the same speed in air regardless of frequency. The key strategy is to compare wavelength to opening size: larger wavelength relative to opening means more diffraction.
Laser light of wavelength $650,\text{nm}$ and $450,\text{nm}$ each passes through the same narrow slit of width $a$. Both beams have the same power. Which light produces the greatest diffraction after the slit?
$450,\text{nm}$ light because its amplitude is larger
$450,\text{nm}$ light because its speed in air is greater
$650,\text{nm}$ light because $\lambda/a$ is larger
$650,\text{nm}$ light because its intensity is higher
Explanation
This question tests understanding of diffraction. Diffraction is the spreading of waves after passing through an opening, with the amount of spreading determined by the ratio λ/a (wavelength to slit width). Since both laser beams pass through the same slit width a, the beam with the larger wavelength will have a larger λ/a ratio and thus greater diffraction. The 650 nm light has a longer wavelength than 450 nm light, so it diffracts more. Choice B incorrectly suggests that light speed varies with wavelength in air, but all electromagnetic waves travel at the same speed c in vacuum or air. Remember: for a fixed opening, longer wavelength means more diffraction.
Light passes through a slit of width $a$ and forms a diffraction pattern on a distant screen. The slit width is reduced to $a/2$ while wavelength and screen distance stay the same. Compared to before, the light spreads out on the screen the most in which case?
With width $a$, because a wider slit increases spreading
With width $a/2$, because $\lambda/a$ increases
With width $a/2$, because the wave speed increases
With width $a$, because intensity is higher
Explanation
This question tests understanding of diffraction. Diffraction is the spreading of light after passing through a slit, with the angular spread determined by the ratio λ/a (wavelength to slit width). When the slit width is reduced from a to a/2, the ratio λ/a doubles, causing the diffraction pattern to spread out more on the screen. The central bright fringe becomes wider and the entire pattern expands. Choice A incorrectly suggests that wider slits cause more spreading, but this confuses the total light transmitted with the angular spreading of the diffraction pattern. Remember: smaller slit width relative to wavelength produces greater diffraction spreading.
A ripple tank sends plane water waves of wavelength $\lambda$ toward four gaps in a barrier. Each gap is illuminated with the same wave speed. The gap widths are: (1) $0.5\lambda$, (2) $\lambda$, (3) $2\lambda$, (4) $4\lambda$. Which gap produces the greatest diffraction (widest spreading) after the barrier?
Gap width $4\lambda$
Gap width $0.5\lambda$
Gap width $\lambda$
Gap width $2\lambda$
Explanation
This question tests understanding of diffraction. Diffraction is the spreading of waves as they pass through an opening or around an obstacle, and the amount of spreading depends on the ratio of wavelength to opening size. When the opening is much larger than the wavelength, waves pass through with minimal bending, but when the opening is comparable to or smaller than the wavelength, significant spreading occurs. The gap with width 0.5λ has the smallest opening relative to the wavelength, producing the greatest diffraction. A common misconception (choice A) is that larger openings cause more diffraction, but this confuses the amount of wave energy passing through with the angular spreading of the wave. Remember: diffraction is strongest when the opening size is comparable to or smaller than the wavelength.
Plane water waves of wavelength $\lambda$ encounter a barrier with a gap of width $w$. In Case 1, $w=\lambda$; in Case 2, $w=5\lambda$. The waves spread after passing through the gap. Which case produces the greatest spreading?
Case 1, because the gap width is comparable to $\lambda$
Case 2, because more wavefront passes through and spreads farther
Case 1, because the intensity is greater when the opening is smaller
Case 2, because the wave speed is higher for larger gaps
Explanation
This question tests understanding of diffraction. Diffraction is the spreading of waves after passing through a gap, with the amount of spreading inversely related to the ratio of gap width to wavelength. When the gap width w equals the wavelength λ (Case 1), significant diffraction occurs because the opening is comparable to the wavelength. When w = 5λ (Case 2), the gap is much wider than the wavelength, resulting in minimal spreading as waves pass through mostly unchanged. Choice A incorrectly assumes that more wavefront passing through leads to more spreading, confusing the amount of wave energy with the geometric spreading angle - this is a common misconception. The strategy to remember is that diffraction effects are strongest when the opening size matches the wavelength.