Middle School Science Quiz: Measure Wave Amplitude
20 questions · exam conditions
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Measure Wave AmplitudeQuestion 1 of 20

On a displacement graph, the wave's maximum displacement is 4 cm-4\text{ cm} (the lowest trough) and the equilibrium line is at 0 cm0\text{ cm}. What is the amplitude of the wave?

4 cm-4\text{ cm}
8 cm8\text{ cm}
4 cm4\text{ cm}
0 cm0\text{ cm}
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Middle School Science Quiz

Middle School Science Quiz: Measure Wave Amplitude

Practice Measure Wave Amplitude in Middle School Science with focused quiz questions that help you check what you know, review explanations, and build confidence with test-style prompts.

What this quiz covers

This quiz focuses on Measure Wave Amplitude, giving you a quick way to practice the rules, question types, and explanations that matter most for Middle School Science.

How to use this quiz

Try each quiz question before looking at the correct answer. Use the explanations to review missed ideas, then come back to similar questions until the pattern feels familiar.

All questions

Question 1

On a displacement graph, the wave's maximum displacement is 4 cm-4\text{ cm} (the lowest trough) and the equilibrium line is at 0 cm0\text{ cm}. What is the amplitude of the wave?

  1. 4 cm-4\text{ cm}
  2. 8 cm8\text{ cm}
  3. 4 cm4\text{ cm} (correct answer)
  4. 0 cm0\text{ cm}
Explanation: This question tests understanding that amplitude is the maximum displacement from the rest (equilibrium) position to the crest or trough, measured as a distance, not the total wave height from crest to trough. When given a trough position and equilibrium position, amplitude is the magnitude (absolute value) of the displacement. For a wave with equilibrium at 0 cm and lowest trough at -4 cm: the displacement from equilibrium (0 cm) to trough (-4 cm) is -4 - 0 = -4 cm, but amplitude is always expressed as positive magnitude, so A = |-4| = 4 cm. This represents the maximum distance the wave moves from its rest position, regardless of direction. If this wave is symmetric, its crest would be at +4 cm, confirming amplitude of 4 cm whether measured to crest or trough. Choice C is correct because it properly identifies the amplitude as 4 cm, the magnitude of the maximum displacement from equilibrium. Choice A gives -4 cm, but amplitude is always positive; Choice B gives 8 cm, which would be the crest-to-trough distance if the wave is symmetric; Choice D incorrectly suggests 0 cm amplitude, which would mean no wave at all.

Question 2

A student measures a wave and finds the vertical distance from crest to trough is 12 cm12\text{ cm}. The equilibrium position is halfway between crest and trough. What is the amplitude?​

  1. 12 cm12\text{ cm}
  2. 24 cm24\text{ cm}
  3. 6 cm6\text{ cm} (correct answer)
  4. 6 cm-6\text{ cm}
Explanation: This question tests understanding that amplitude is the maximum displacement from the rest (equilibrium) position to the crest or trough, measured as a distance, not the total wave height from crest to trough. Amplitude is defined as the maximum distance a wave moves from its rest/equilibrium position: when given that the crest-to-trough distance is 12 cm and the equilibrium position is halfway between them, the amplitude is half this distance. If equilibrium is halfway between crest and trough, then the crest is 6 cm above equilibrium and the trough is 6 cm below equilibrium, making the amplitude 6 cm. This makes sense because crest-to-trough distance equals 2A (twice the amplitude): if 2A = 12 cm, then A = 6 cm. A common mistake is using the full crest-to-trough distance as amplitude, but this gives twice the amplitude (2A), not the amplitude itself—amplitude is always measured from the rest position to the peak, not peak to peak. Choice C is correct because it correctly calculates amplitude as half the crest-to-trough distance: with equilibrium halfway between crest and trough, and crest-to-trough = 12 cm, the crest is 6 cm above equilibrium (and trough 6 cm below), so amplitude = 6 cm. Choice A (12 cm) incorrectly uses the full crest-to-trough distance as amplitude when that's 2A; Choice B (24 cm) incorrectly doubles the crest-to-trough distance; Choice D (-6 cm) uses negative value when amplitude is magnitude (6 cm positive). Measuring wave amplitude from crest-to-trough information: (1) identify that equilibrium is halfway between crest and trough (given), (2) recognize that crest-to-trough distance = 2A (twice amplitude), (3) calculate amplitude: A = (crest-to-trough distance)/2 = 12 cm/2 = 6 cm, (4) verify: if amplitude is 6 cm, then crest is +6 cm and trough is -6 cm from equilibrium, giving crest-to-trough = 6 - (-6) = 12 cm ✓. Understanding this relationship helps convert between different wave measurements: knowing any one of amplitude (A), crest-to-trough distance (2A), or positions of crest/trough relative to equilibrium allows calculation of the others.

Question 3

A wave's equilibrium (rest) position is a straight line halfway between the crest and trough. If the trough is at 7 cm-7\text{ cm} (relative to equilibrium), what is the amplitude?​

  1. 7 cm-7\text{ cm}
  2. 14 cm14\text{ cm}
  3. 7 cm7\text{ cm} (correct answer)
  4. 0 cm0\text{ cm}
Explanation: This question tests understanding that amplitude is the maximum displacement from the rest (equilibrium) position to the crest or trough, measured as a distance, not the total wave height from crest to trough. Amplitude is defined as the maximum distance a wave moves from its rest/equilibrium position: when the trough is at -7 cm relative to equilibrium (meaning 7 cm below the equilibrium line), the amplitude is the magnitude of this displacement, which is 7 cm. The negative sign indicates direction (below equilibrium) but amplitude is always expressed as a positive magnitude. For a symmetric wave with equilibrium halfway between crest and trough, if the trough is -7 cm from equilibrium, the crest would be +7 cm from equilibrium, confirming amplitude of 7 cm. A common mistake is keeping the negative sign, but amplitude represents magnitude of maximum displacement regardless of direction. Choice C is correct because it correctly identifies amplitude as the magnitude of displacement from equilibrium to trough: with trough at -7 cm from equilibrium, amplitude = |-7| = 7 cm (the maximum displacement magnitude). Choice A (-7 cm) incorrectly keeps the negative sign when amplitude is always positive magnitude; Choice B (14 cm) incorrectly doubles the amplitude, perhaps thinking of crest-to-trough distance (which would be 2A = 14 cm for a symmetric wave); Choice D (0 cm) incorrectly suggests no amplitude when the wave clearly has a trough 7 cm below equilibrium. Measuring amplitude from trough information: (1) identify that trough is at -7 cm relative to equilibrium (7 cm below), (2) recognize amplitude is magnitude of this displacement, (3) calculate amplitude = |-7| = 7 cm (remove negative sign), (4) verify: for symmetric wave, crest would be +7 cm from equilibrium, also giving amplitude of 7 cm. Understanding that amplitude is always positive prevents sign errors when working with troughs (negative displacements).

Question 4

A student measures the vertical distance from the crest of a wave to the trough and gets 12 cm. The rest position is halfway between crest and trough. What is the amplitude of the wave?

  1. 12 cm
  2. 6 cm (correct answer)
  3. 3 cm
  4. -6 cm
Explanation: This question tests understanding that amplitude is the maximum displacement from the rest (equilibrium) position to the crest or trough, measured as a distance, not the total wave height from crest to trough. Amplitude is defined as the maximum distance a wave moves from its rest/equilibrium position: if crest-to-trough is 12 cm and rest is halfway, then from rest to crest is 6 cm (half of 12 cm) and rest to trough is 6 cm, so amplitude is 6 cm—assuming symmetry where rest is midway. A common mistake is taking the full 12 cm as amplitude instead of half, or halving incorrectly to 3 cm, or using negative values. Choice B is correct because it recognizes that with rest halfway, amplitude is half the crest-to-trough distance (12 cm / 2 = 6 cm), accurately measuring maximum displacement from equilibrium. Choice A uses the full 12 cm, confusing with 2A; Choice C quarters to 3 cm mistakenly; Choice D uses negative (-6 cm) when amplitude is positive magnitude. Measuring wave amplitude systematically: (1) locate rest (halfway between crest and trough), (2) identify max point (crest or trough), (3) measure distance from rest (6 cm), (4) record A=6 cm, and (5) verify (total height 12 cm = 2A, yes). Amplitude significance: 6 cm amplitude means more energy (E ∝ A²) than smaller waves, important for understanding wave impact like in oceans.

Question 5

A wave is shown on a graph with a clearly marked equilibrium line at y=0 cmy=0\text{ cm}. The crest is at y=+4 cmy=+4\text{ cm} and the trough is at y=4 cmy=-4\text{ cm}. Which statement correctly describes how to measure the amplitude?

  1. Measure from crest to trough to get the amplitude: 8 cm8\text{ cm}
  2. Measure from the equilibrium line to the crest (or to the trough): 4 cm4\text{ cm} (correct answer)
  3. Measure from one crest to the next crest to get amplitude
  4. Amplitude is the signed value at the trough: 4 cm-4\text{ cm}
Explanation: This question tests understanding that amplitude is the maximum displacement from the rest (equilibrium) position to the crest or trough, measured as a distance, not the total wave height from crest to trough. Amplitude is defined as the maximum distance a wave moves from its rest/equilibrium position: from y=0 to +4 cm (crest) or to -4 cm (trough) gives A=4 cm. For wave on graph: Rest at y=0, crest +4 cm, trough -4 cm, amplitude is the vertical distance from equilibrium to either extreme (4 cm). Choice B is correct because it describes measuring from the equilibrium line to the crest or trough (4 cm), accurately identifying the method. Choice A measures crest to trough (8 cm=2A); Choice C describes wavelength; Choice D uses signed trough value. Measuring wave amplitude systematically: (1) locate equilibrium (y=0), (2) identify extreme (crest +4 cm), (3) measure distance (4 cm), (4) record A=4 cm positive, and (5) verify with trough (same). This reinforces correct procedure, avoiding common pitfalls like peak-to-peak measurement or negative values.

Question 6

A water wave passes by a dock. The water surface at rest is the equilibrium position. The highest point of the wave is 5 cm5\text{ cm} above the calm surface and the lowest point is 5 cm5\text{ cm} below it. What is the amplitude of the wave?

  1. 10 cm10\text{ cm}
  2. 5 cm5\text{ cm} (correct answer)
  3. 2.5 cm2.5\text{ cm}
  4. 5 cm-5\text{ cm}
Explanation: This question tests understanding that amplitude is the maximum displacement from the rest (equilibrium) position to the crest or trough, measured as a distance, not the total wave height from crest to trough. Amplitude is defined as the maximum distance a wave moves from its rest/equilibrium position: for a water wave, the rest position is the calm surface, the crest is the highest point (5 cm above calm), and the amplitude is the distance from rest to crest (A=5 cm). The trough (5 cm below calm) also gives A=5 cm magnitude, confirming consistency for symmetric waves. Choice B is correct because it measures amplitude as 5 cm, the maximum displacement from the equilibrium calm surface to the crest or trough. Choice A is wrong because it adds crest and trough for total height (10 cm=2A); Choice C halves incorrectly (2.5 cm); Choice D uses negative when amplitude is positive. Measuring wave amplitude systematically: (1) locate rest/equilibrium (calm surface), (2) identify maximum point (crest 5 cm above), (3) measure distance (5 cm), (4) record A=5 cm, and (5) verify with trough (5 cm below, same magnitude). Larger amplitude means taller wave: 5 cm amplitude is taller than 2 cm, carrying (5/2)²=6.25× more energy, emphasizing correct measurement to avoid mistaking total height for amplitude.

Question 7

On a displacement vs. position graph, the equilibrium line is labeled y=0 cmy=0\text{ cm}. Each grid square represents 1 cm1\text{ cm} vertically. A crest is 4 squares above the equilibrium line. What is the amplitude?

  1. 8 cm8\text{ cm}
  2. 4 cm4\text{ cm} (correct answer)
  3. 1 cm1\text{ cm}
  4. 4 cm4\text{ cm} horizontally (wavelength)
Explanation: This question tests understanding that amplitude is the maximum displacement from the rest (equilibrium) position to the crest or trough, measured as a distance, not the total wave height from crest to trough. Amplitude is defined as the maximum distance a wave moves from its rest/equilibrium position: on a graph, rest is y=0, crest 4 squares above (each 1 cm, so +4 cm), giving A=4 cm from y=0 to +4 cm. For wave on graph: A wave with rest at y=0, crest at y=+4 cm, has amplitude A=4 cm measured vertically from equilibrium to crest. Choice B is correct because it properly uses the scale (4 squares × 1 cm/square=4 cm) to measure displacement from equilibrium to crest. Choice A measures total height (8 cm=2A); Choice C ignores scale (1 cm instead of 4); Choice D confuses horizontal wavelength with vertical amplitude. Measuring wave amplitude systematically: (1) locate equilibrium (y=0), (2) identify crest (4 squares above), (3) measure using scale (4×1 cm=4 cm), (4) record A=4 cm, and (5) verify consistency. Understanding correct measurement prevents errors like misreading grid scales or confusing amplitude with wavelength.

Question 8

A pendulum's equilibrium position is straight down at θ=0\theta=0^\circ. It swings to a maximum of 1515^\circ to the left and 1515^\circ to the right. What is the amplitude of the pendulum's motion?

  1. 3030^\circ (left to right)
  2. 1515^\circ (correct answer)
  3. 00^\circ
  4. 15-15^\circ
Explanation: This question tests understanding that amplitude is the maximum displacement from the rest (equilibrium) position to the crest or trough, measured as a distance, not the total wave height from crest to trough. Amplitude is defined as the maximum distance a wave moves from its rest/equilibrium position: for a pendulum, rest is θ=0°, max swing to 15° (left or right), giving A=15°. Like a transverse wave, the 'crest' is max angle one side (+15°), trough the other (-15°), but amplitude is the max displacement magnitude (15°). Choice B is correct because it measures the maximum angular displacement from equilibrium (15°), treating left and right symmetrically. Choice A adds total swing (30°=2A); Choice C is equilibrium itself; Choice D is negative. Measuring wave amplitude systematically: (1) locate equilibrium (0°), (2) identify max displacement (15°), (3) measure angle (15°), (4) record A=15°, and (5) verify both sides same. Amplitude significance in pendulums: larger A means wider swing, more energy, preventing confusion of total arc with amplitude.

Question 9

A transverse wave is drawn on a graph where the equilibrium (rest) position is the horizontal line at y=0 cmy=0\text{ cm}. The crest reaches y=+3 cmy=+3\text{ cm} and the trough reaches y=3 cmy=-3\text{ cm}. What is the amplitude of the wave?

  1. 6 cm6\text{ cm} (crest to trough)
  2. 3 cm-3\text{ cm}
  3. 3 cm3\text{ cm} (rest to crest) (correct answer)
  4. 3 cm3\text{ cm} (crest to trough divided by 3)
Explanation: This question tests understanding that amplitude is the maximum displacement from the rest (equilibrium) position to the crest or trough, measured as a distance, not the total wave height from crest to trough. Amplitude is defined as the maximum distance a wave moves from its rest/equilibrium position: for a transverse wave on a graph, the rest position is typically the center horizontal line (y = 0 or the middle), the crest is the highest point (maximum positive displacement, like y = +3 cm), and the amplitude is the distance from rest to crest (measuring vertically from y = 0 to y = +3 gives A = 3 cm). The trough (lowest point, like y = -3 cm) is also 3 cm from rest (measuring from y = 0 to y = -3, the magnitude is 3 cm), confirming amplitude is 3 cm—it's the same whether measured to crest or to trough because waves are typically symmetric about equilibrium. Choice C is correct because it accurately measures amplitude as the distance from rest to crest (3 cm), properly identifying the equilibrium at y=0 and using the maximum displacement. Choice A is wrong because it measures crest to trough (6 cm), which is twice the amplitude (2A), not the amplitude itself; Choice B uses a negative value (-3 cm) when amplitude is a positive magnitude; Choice D incorrectly divides the crest-to-trough distance by 3 instead of 2. Measuring wave amplitude systematically: (1) locate rest/equilibrium position (y=0 line), (2) identify maximum displacement point (crest at +3 cm), (3) measure distance from rest to that point (3 cm), (4) record as amplitude with units (A=3 cm, positive), and (5) verify with trough (also 3 cm magnitude). Amplitude significance: indicates wave energy (E ∝ A²: A=3 cm has 9× more energy than A=1 cm), and understanding correct measurement prevents errors like confusing 2A with A.

Question 10

A student measures the vertical distance from the crest of a wave to the trough and gets 8 cm8\text{ cm}. The wave is symmetric about its equilibrium (rest) position. What is the amplitude?

  1. 8 cm8\text{ cm}
  2. 4 cm4\text{ cm} (correct answer)
  3. 16 cm16\text{ cm}
  4. 4 cm-4\text{ cm}
Explanation: This question tests understanding that amplitude is the maximum displacement from the rest (equilibrium) position to the crest or trough, measured as a distance, not the total wave height from crest to trough. Amplitude is defined as the maximum distance a wave moves from its rest/equilibrium position: if crest-to-trough is 8 cm and symmetric, then A=4 cm (half the total height). For symmetric waves, the total wave height (crest to trough) is 2A, so measuring 8 cm gives A=8/2=4 cm. Choice B is correct because it recognizes the given crest-to-trough distance as 2A and halves it for amplitude (4 cm). Choice A uses total height as A; Choice C doubles incorrectly; Choice D is negative. Measuring wave amplitude systematically: (1) confirm symmetry about equilibrium, (2) measure total height (8 cm), (3) divide by 2 (4 cm), (4) record A=4 cm, and (5) verify consistency. This method is useful when only total height is given, preventing the common mistake of equating total height with amplitude.

Question 11

A wave is drawn on grid paper. The equilibrium line is the middle horizontal line labeled y=0 cmy=0\text{ cm}. Each grid square represents 1 cm1\text{ cm} vertically. The crest is 4 squares above the equilibrium line. What is the amplitude?

  1. 8 cm
  2. 4 cm (correct answer)
  3. 2 cm
  4. 4 squares (no units)
Explanation: This question tests understanding that amplitude is the maximum displacement from the rest (equilibrium) position to the crest or trough, measured as a distance, not the total wave height from crest to trough. Amplitude is defined as the maximum distance a wave moves from its rest/equilibrium position: on grid paper, rest is the middle line at y=0 cm, the crest is 4 squares above (each 1 cm, so +4 cm), and amplitude is the distance from rest to crest (4 cm)—if there's a trough, it would confirm, but crest measurement suffices. A common mistake is measuring from some other reference or forgetting the scale, like counting squares without units or doubling for total height. Choice B is correct because it properly uses the scale (4 squares × 1 cm/square = 4 cm) to measure displacement from equilibrium to crest, accurately identifying rest at the middle line. Choice A might double it to 8 cm thinking crest-to-trough; Choice C halves to 2 cm incorrectly; Choice D omits units, just giving squares, but amplitude needs units like cm. Measuring wave amplitude systematically: (1) locate rest (middle line y=0), (2) identify max point (crest 4 squares up), (3) measure using scale (4 × 1 cm = 4 cm), (4) record A=4 cm, and (5) verify if trough shown (would be same if symmetric). Amplitude significance: 4 cm amplitude indicates energy level (E ∝ A²), useful in contexts like rope waves where larger A means more vigorous shaking.

Question 12

Two waves are compared using the same vertical scale (in cm) with the rest position at y=0y=0. Wave A has a crest at +2 cm+2\text{ cm} and a trough at 2 cm-2\text{ cm}. Wave B has a crest at +5 cm+5\text{ cm} and a trough at 5 cm-5\text{ cm}. Which statement is correct?

  1. Wave A has larger amplitude because 2 cm is greater than 5 cm.
  2. Wave B has larger amplitude because 5 cm is greater than 2 cm. (correct answer)
  3. Both waves have the same amplitude because both cross the rest position.
  4. Neither wave has an amplitude because amplitude is measured crest-to-trough.
Explanation: This question tests understanding that amplitude is the maximum displacement from the rest (equilibrium) position to the crest or trough, measured as a distance, not the total wave height from crest to trough. Amplitude is defined as the maximum distance a wave moves from its rest/equilibrium position: both waves have rest at y=0, Wave A has crest at +2 cm (A=2 cm) and trough at -2 cm, while Wave B has crest at +5 cm (A=5 cm) and trough at -5 cm, so Wave B's amplitude (5 cm) is larger than Wave A's (2 cm) since 5 > 2. A common mistake is measuring from crest to trough and comparing totals (Wave A: 4 cm, Wave B: 10 cm), but amplitude is half that for symmetric waves—still Wave B larger—or reversing which is bigger. Choice B is correct because it properly identifies Wave B's amplitude as 5 cm (rest to +5 cm) which is greater than Wave A's 2 cm (rest to +2 cm), using the same scale and rest position. Choice A reverses the comparison, claiming 2 cm > 5 cm incorrectly; Choice C assumes same amplitude because both cross rest, ignoring actual displacements; Choice D wrongly states neither has amplitude, confusing with crest-to-trough measurement which is actually 2A. Measuring wave amplitude systematically: (1) locate rest (y=0), (2) identify max displacement (Wave A: 2 cm, Wave B: 5 cm), (3) measure from rest, (4) record A, and (5) compare magnitudes (5 cm > 2 cm). Amplitude significance: Wave B has larger amplitude, thus more energy (E ∝ A², (5/2)²=6.25× more than A), making it 'taller' and more intense.

Question 13

A sound wave is shown on a pressure vs. time graph. The rest position (equilibrium) is atmospheric pressure, and the wave reaches a maximum of +10 Pa+10\text{ Pa} above atmospheric and a minimum of 10 Pa-10\text{ Pa} below atmospheric. What is the amplitude of this sound wave (maximum pressure variation from equilibrium)?

  1. 20 Pa
  2. 10 Pa (correct answer)
  3. -10 Pa
  4. 101,325 Pa
Explanation: This question tests understanding that amplitude is the maximum displacement from the rest (equilibrium) position to the crest or trough, measured as a distance, not the total wave height from crest to trough. Amplitude is defined as the maximum distance a wave moves from its rest/equilibrium position: for a sound wave on a pressure graph, the rest position is atmospheric pressure, the maximum is +10 Pa above (compression peak), and the amplitude is the distance from rest to peak (10 Pa); the minimum -10 Pa below (rarefaction) is also 10 Pa from rest (magnitude), confirming amplitude is 10 Pa—it's the same whether measured to max or min because the wave is symmetric. A common mistake is measuring from max to min (+10 to -10 = 20 Pa total), but this gives twice the amplitude (2A), not the amplitude itself—amplitude is always measured from the rest position to the peak, not peak to peak. Choice B is correct because it accurately measures amplitude as the maximum pressure variation from equilibrium (atmospheric) to the peak (+10 Pa) or to the minimum (-10 Pa), using the magnitude (10 Pa). Choice A measures total range (20 Pa) calling it amplitude when that's 2A; Choice C uses negative (-10 Pa) when amplitude is positive magnitude; Choice D confuses rest pressure (101,325 Pa) with amplitude, which is the deviation. Measuring wave amplitude systematically: (1) locate rest/equilibrium (atmospheric pressure line), (2) identify maximum displacement (+10 Pa or -10 Pa), (3) measure distance from rest (10 Pa), (4) record as A=10 Pa, and (5) verify symmetry (both sides 10 Pa). Amplitude significance: larger pressure amplitude means louder sound and more energy (E ∝ A², 10 Pa is 100× energy of 1 Pa), determining intensity.

Question 14

A pendulum swings back and forth. Its equilibrium position is straight down at θ=0\theta=0^\circ. The pendulum reaches a maximum angle of 1515^\circ to the left and 1515^\circ to the right. What is the amplitude of the pendulum's motion?

  1. 30°
  2. 15° (correct answer)
  3. -15°
Explanation: This question tests understanding that amplitude is the maximum displacement from the rest (equilibrium) position to the crest or trough, measured as a distance, not the total wave height from crest to trough. Amplitude is defined as the maximum distance a wave moves from its rest/equilibrium position: for a pendulum, the rest position is straight down at θ=0°, the maximum to the right is +15° (one peak), and the amplitude is the distance from rest to that max (15°); the left max at -15° is also 15° from rest (magnitude), confirming amplitude is 15°—it's the same on both sides due to symmetry. A common mistake is measuring from left to right (-15° to +15° = 30° total), but this gives twice the amplitude (2A), not the amplitude itself—amplitude is always measured from the rest position to the peak, not peak to peak. Choice B is correct because it accurately measures amplitude as the maximum angular displacement from equilibrium (0°) to the peak (15° to left or right), using the magnitude. Choice A measures total swing (30°) calling it amplitude when that's 2A; Choice C uses negative (-15°) when amplitude is positive; Choice D assumes no amplitude at rest, ignoring max deviation. Measuring wave amplitude systematically: (1) locate rest (θ=0°), (2) identify max displacement (15° left or right), (3) measure from rest (15°), (4) record A=15°, and (5) verify both sides equal. Amplitude significance: larger amplitude means wider swing and more energy (E ∝ A²), affecting pendulum motion like period approximation for small angles.

Question 15

A water wave moves across a pool. The calm water level is the equilibrium (rest) position. At one moment, the crest is 5 cm above the calm level and the trough is 5 cm below the calm level. What is the wave's amplitude?

  1. 10 cm
  2. 5 cm (correct answer)
  3. -5 cm
  4. 2.5 cm
Explanation: This question tests understanding that amplitude is the maximum displacement from the rest (equilibrium) position to the crest or trough, measured as a distance, not the total wave height from crest to trough. Amplitude is defined as the maximum distance a wave moves from its rest/equilibrium position: for a water wave, the rest position is the calm water level, the crest is 5 cm above calm (maximum positive displacement), and the amplitude is the distance from rest to crest (5 cm); the trough 5 cm below calm is also 5 cm from rest (magnitude), confirming amplitude is 5 cm—it's the same whether measured to crest or to trough because the wave is symmetric. A common mistake is measuring from crest to trough (5 + 5 = 10 cm total), but this gives twice the amplitude (2A), not the amplitude itself—amplitude is always measured from the rest position to the peak, not peak to peak. Choice B is correct because it accurately measures amplitude as the distance from the calm level (rest) to the crest (5 cm above) or to the trough (5 cm below), using the magnitude of the maximum displacement. Choice A measures crest to trough (10 cm) calling it amplitude when that's 2A, and amplitude is 5 cm; Choice C uses a negative value (-5 cm) when amplitude is positive (5 cm); Choice D halves it incorrectly to 2.5 cm, perhaps confusing with average. Measuring wave amplitude systematically: (1) locate rest/equilibrium position (calm water level), (2) identify maximum displacement point (crest 5 cm above), (3) measure distance from rest to that point (5 cm), (4) record as amplitude with units (A=5 cm), and (5) verify with trough (also 5 cm). Amplitude significance: larger amplitude means taller wave and more energy (E ∝ A², so 5 cm amplitude has (5/2)²=6.25× more energy than 2 cm), affecting physical impact like wave power.

Question 16

A student measures a wave and says: "The crest is at +4 cm+4\text{ cm} and the trough is at 4 cm-4\text{ cm}, so the amplitude is 8 cm8\text{ cm}." Which response correctly fixes the mistake?

  1. The student is correct: amplitude is always crest-to-trough.
  2. Amplitude should be negative for troughs, so the amplitude is 4 cm-4\text{ cm}.
  3. Amplitude is measured from equilibrium to a crest (or trough), so the amplitude is 4 cm4\text{ cm}. (correct answer)
  4. Amplitude is the horizontal distance from one crest to the next.
Explanation: This question tests understanding that amplitude is the maximum displacement from the rest (equilibrium) position to the crest or trough, measured as a distance, not the total wave height from crest to trough. Amplitude is defined as the maximum distance a wave moves from its rest/equilibrium position: the student's measurement of +4 cm to -4 cm totals 8 cm, which is 2A, but actual amplitude is 4 cm from rest to crest. The wave is symmetric, so trough also gives 4 cm magnitude; a common mistake is measuring crest-to-trough as amplitude, but amplitude is rest-to-peak. Choice C is correct because it explains amplitude is measured from equilibrium to crest (or trough), giving 4 cm. Choice A agrees with the mistake (crest-to-trough as amplitude); Choice B suggests negative for troughs incorrectly (amplitude positive); Choice D confuses with wavelength (horizontal distance). Measuring wave amplitude systematically: (1) locate equilibrium (center), (2) identify crest (+4 cm), (3) measure from rest (4 cm), (4) record A=4 cm, and (5) verify with trough (4 cm). Correcting this prevents overestimating energy (E ∝ A²: true A=4 cm has 16× for 1 cm, but mistaken 8 cm would inflate to 64×).

Question 17

A transverse wave is drawn on a graph. The equilibrium (rest) position is the horizontal line at y=0 cmy=0\text{ cm}. The crest reaches y=+3 cmy=+3\text{ cm} and the trough reaches y=3 cmy=-3\text{ cm}. What is the amplitude of the wave?

  1. 6 cm6\text{ cm} (crest to trough)
  2. 3 cm-3\text{ cm}
  3. 3 cm3\text{ cm} (correct answer)
  4. 0 cm0\text{ cm}
Explanation: This question tests understanding that amplitude is the maximum displacement from the rest (equilibrium) position to the crest or trough, measured as a distance, not the total wave height from crest to trough. Amplitude is defined as the maximum distance a wave moves from its rest/equilibrium position: for a transverse wave on a graph, the rest position is typically the center horizontal line (y = 0 cm), the crest is the highest point (maximum positive displacement, like y = +3 cm), and the amplitude is the distance from rest to crest (measuring vertically from y = 0 to y = +3 gives A = 3 cm). The trough (lowest point, like y = -3 cm) is also 3 cm from rest (measuring from y = 0 to y = -3, the magnitude is 3 cm), confirming amplitude is 3 cm—it's the same whether measured to crest or to trough because waves are typically symmetric about equilibrium; a common mistake is measuring from crest to trough (from +3 to -3 = 6 cm total), but this gives twice the amplitude (2A), not the amplitude itself—amplitude is always measured from the rest position to the peak, not peak to peak. Choice C is correct because it accurately identifies the amplitude as 3 cm, measuring the distance from the equilibrium at y=0 cm to the crest at +3 cm (or trough at -3 cm). Choice A measures crest to trough (6 cm) calling it amplitude when that's 2A, and amplitude is rest to crest (3 cm); Choice B uses a negative value (-3 cm) when amplitude is a magnitude (3 cm positive); Choice D incorrectly states 0 cm, ignoring the displacements. Measuring wave amplitude systematically: (1) locate rest/equilibrium position (the center line, y = 0), (2) identify maximum displacement point (crest at +3 cm), (3) measure distance from rest to that point (3 cm), (4) record as amplitude with units (A = 3 cm, positive), and (5) verify with trough (also 3 cm). Amplitude significance: indicates wave energy (E ∝ A²: A=3 cm has 9× more energy than A=1 cm), and understanding correct measurement prevents errors like confusing with total height.

Question 18

A wave is drawn on grid paper where each vertical grid square represents 1 cm1\text{ cm}. The equilibrium line is the middle horizontal line. A crest is 4 squares above equilibrium and a trough is 4 squares below equilibrium. What is the amplitude of the wave?

  1. 8 cm8\text{ cm}
  2. 4 cm4\text{ cm} (correct answer)
  3. 2 cm2\text{ cm}
  4. 4 cm-4\text{ cm}
Explanation: This question tests understanding that amplitude is the maximum displacement from the rest (equilibrium) position to the crest or trough, measured as a distance, not the total wave height from crest to trough. Amplitude is defined as the maximum distance a wave moves from its rest/equilibrium position: for a wave on grid paper, the rest position is the middle horizontal line, a crest 4 squares above means maximum positive displacement, and with each square 1 cm, amplitude is 4 cm from rest to crest. The trough 4 squares below is also 4 cm from rest (magnitude), confirming amplitude is 4 cm—it's the same whether measured to crest or to trough because waves are typically symmetric about equilibrium; a common mistake is measuring from crest to trough (8 squares = 8 cm total), but this gives twice the amplitude (2A), not the amplitude itself—amplitude is always measured from the rest position to the peak, not peak to peak. Choice B is correct because it properly uses the scale to measure displacement (4 squares × 1 cm/square = 4 cm) from the equilibrium line to the crest (or trough). Choice A measures crest to trough (8 cm) calling it amplitude when that's 2A, amplitude is 4 cm; Choice C halves incorrectly to 2 cm; Choice D uses a negative value (-4 cm) when amplitude is positive magnitude. Measuring wave amplitude systematically: (1) locate rest/equilibrium position (middle horizontal line), (2) identify maximum displacement point (crest 4 squares above), (3) measure distance (count squares: 4 × 1 cm = 4 cm), (4) record as amplitude (A = 4 cm), and (5) verify with trough (also 4 cm). Common measurement contexts: on grid paper, ensure scale is applied correctly (here 1 cm/square), and amplitude indicates energy (E ∝ A²: 4 cm has 16× more than 1 cm), preventing errors like miscounting squares or confusing with total height.

Question 19

A sound wave is shown on a pressure-vs-time graph. The equilibrium pressure (center line) is atmospheric pressure. The compression peaks reach +10 Pa+10\text{ Pa} above atmospheric pressure, and rarefactions reach 10 Pa-10\text{ Pa} below atmospheric pressure. What is the amplitude of this sound wave (maximum pressure variation from equilibrium)?

  1. 20 Pa20\text{ Pa}
  2. 10 Pa10\text{ Pa} (correct answer)
  3. 0 Pa0\text{ Pa}
  4. 10 Pa-10\text{ Pa}
Explanation: This question tests understanding that amplitude is the maximum displacement from the rest (equilibrium) position to the crest or trough, measured as a distance, not the total wave height from crest to trough. Amplitude is defined as the maximum distance a wave moves from its rest/equilibrium position: for a sound wave on a pressure graph, the rest is atmospheric pressure (center line), compression peak at +10 Pa means amplitude is 10 Pa from rest to peak. Rarefaction at -10 Pa is also 10 Pa from rest (magnitude), confirming amplitude is 10 Pa—it's the same whether measured to compression or rarefaction because waves are typically symmetric; a common mistake is measuring from peak to trough (20 Pa total), but this gives twice the amplitude (2A), not the amplitude itself—amplitude is always measured from the rest position to the peak, not peak to peak. Choice B is correct because it measures the maximum pressure variation from equilibrium (10 Pa) accurately. Choice A measures peak to trough (20 Pa) calling it amplitude when that's 2A; Choice C incorrectly states 0 Pa; Choice D uses negative (-10 Pa) when amplitude is positive magnitude. Measuring wave amplitude systematically: (1) locate rest/equilibrium (atmospheric pressure line), (2) identify maximum displacement ( +10 Pa), (3) measure distance (10 Pa), (4) record as amplitude (A = 10 Pa), and (5) verify with rarefaction (also 10 Pa). Larger pressure amplitude means louder sound: 10 Pa is louder than 1 Pa (100× more energy, E ∝ A²), and correct measurement prevents errors in sound intensity calculations.

Question 20

A wave is drawn on a graph where the vertical axis is labeled in centimeters. The equilibrium line is at y=1 cmy=1\text{ cm}. A crest is at y=5 cmy=5\text{ cm} and a trough is at y=3 cmy=-3\text{ cm}. What is the amplitude of the wave?

  1. 4 cm4\text{ cm} (correct answer)
  2. 8 cm8\text{ cm}
  3. 5 cm5\text{ cm}
  4. 1 cm1\text{ cm}
Explanation: This question tests understanding that amplitude is the maximum displacement from the rest (equilibrium) position to the crest or trough, measured as a distance, not the total wave height from crest to trough. Amplitude is defined as the maximum distance a wave moves from its rest/equilibrium position: here equilibrium is at y=1 cm, crest at y=5 cm (displacement +4 cm), trough at y=-3 cm (displacement -4 cm), so amplitude is 4 cm (maximum magnitude). The wave is symmetric in displacement (±4 cm) despite offset labels; a common mistake is measuring from crest to trough (5 - (-3)=8 cm) for 2A, or using labels without subtracting equilibrium. Choice A is correct because it calculates maximum displacement from equilibrium ( |5-1|=4 cm or |-3-1|=4 cm). Choice B measures crest to trough (8 cm) calling it amplitude when that's 2A; Choice C uses crest label (5 cm) without subtracting equilibrium; Choice D uses equilibrium (1 cm) incorrectly. Measuring wave amplitude systematically: (1) locate rest (y=1 cm), (2) identify max points (5 cm and -3 cm), (3) measure displacements (4 cm and 4 cm), (4) take maximum magnitude (A=4 cm), and (5) verify consistency. Understanding offset equilibrium prevents errors, and amplitude indicates energy regardless of reference point.