Measure Wave Amplitude - Middle School Physical Science

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 $+10\text{ Pa}$ above atmospheric and a minimum of $-10\text{ Pa}$ below atmospheric. What is the amplitude of this sound wave (maximum pressure variation from equilibrium)?
Answer: 10 Pa 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.
A transverse wave is drawn on a graph where the equilibrium (rest) position is the horizontal line at $y=0\text{ cm}$ . The crest reaches $y=+4\text{ cm}$ and the trough reaches $y=-4\text{ cm}$ . What is the amplitude of the wave?
Answer: $4\text{ cm}$ 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 = +4 cm), and the amplitude is the distance from rest to crest (measuring vertically from y = 0 to y = +4 gives A = 4 cm). The trough (lowest point, like y = -4 cm) is also 4 cm from rest (measuring from y = 0 to y = -4, the magnitude is 4 cm), 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 (from +4 to -4 = 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 C is correct because it correctly measures amplitude as distance from rest to crest: the wave has equilibrium at y = 0 cm, crest at y = +4 cm, so amplitude = |+4 - 0| = 4 cm (the maximum displacement from equilibrium). Choice A (8 cm) measures crest to trough (+4 to -4 = 8 cm) calling it amplitude when that's 2A, amplitude is rest to crest (4 cm); Choice B (-4 cm) uses negative value when amplitude is magnitude (4 cm positive); Choice D (0 cm) incorrectly suggests no amplitude when the wave clearly displaces ±4 cm from equilibrium. Measuring wave amplitude systematically: (1) locate rest/equilibrium position (here clearly stated as y = 0 cm horizontal line), (2) identify maximum displacement point (crest at y = +4 cm or trough at y = -4 cm—either works), (3) measure distance from rest to that maximum point (from y = 0 to y = +4 is 4 cm), (4) record as amplitude with units (A = 4 cm, always positive magnitude), and (5) verify if possible (check trough: from y = 0 to y = -4 is also 4 cm magnitude ✓ confirming measurement).
A wave has an equilibrium (rest) position at $y=0\text{ m}$ . The crest is at $y=+0.20\text{ m}$ . What does the amplitude represent in this situation, and what is its value?
Answer: The maximum displacement from equilibrium; $0.20\text{ m}$ 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 rest at y=0 m, crest at +0.20 m, so A=0.20 m (maximum displacement). Assuming symmetry, trough at -0.20 m would give 0.40 m as 2A; a common mistake is confusing with crest-to-trough or wavelength. Choice A is correct because it defines amplitude as maximum displacement from equilibrium and gives 0.20 m accurately. Choice B says distance from crest to trough (0.40 m=2A) incorrectly as amplitude; Choice C confuses with wavelength; Choice D uses signed negative (-0.20 m) when amplitude is positive magnitude. Measuring wave amplitude systematically: (1) locate rest (y=0 m), (2) identify crest (+0.20 m), (3) measure distance (0.20 m), (4) record A=0.20 m, and (5) verify if trough given (would be 0.20 m magnitude). Amplitude represents energy carrier (E ∝ A²), distinguishing from other properties like wavelength.
A student says: "The amplitude of a wave is the distance from the crest to the trough." Which correction is best?
Answer: Amplitude is the maximum distance from the rest (equilibrium) position to a crest or to a trough. 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. The student's error is defining amplitude as the crest-to-trough distance, which is actually twice the amplitude (2A) for symmetric waves. Amplitude is correctly defined as the maximum distance from the rest/equilibrium position to a crest or to a trough—this is half the crest-to-trough distance for symmetric waves. For example, a wave with rest at y = 0, crest at +3 cm, and trough at -3 cm has amplitude A = 3 cm (rest to crest), not 6 cm (crest to trough). Choice B is correct because it provides the accurate definition: amplitude is the maximum distance from the rest (equilibrium) position to a crest or to a trough. Choice A incorrectly defines amplitude as wavelength (horizontal distance between crests); Choice C incorrectly defines amplitude as period (time measurement); Choice D incorrectly suggests the crest-to-trough definition applies only to water waves, when actually amplitude is always measured from equilibrium regardless of wave type.
A pendulum hangs straight down at rest (equilibrium position is $\theta=0^\circ$ ). It swings to a maximum of $15^\circ$ to the left and $15^\circ$ to the right. What is the amplitude of the pendulum's motion?
Answer: $15^\circ$ 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, equilibrium is straight down at θ=0°, swinging to +15° means amplitude is 15° from rest to maximum. Swinging to -15° is also 15° from rest (magnitude), confirming amplitude is 15°—it's the same whether measured to left or right because motion is symmetric; a common mistake is measuring total swing (30°), 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 (15°). Choice A measures total from left to right (30°) calling it amplitude when that's 2A; Choice C states 0° incorrectly; Choice D uses negative (-15°) when amplitude is positive magnitude. Measuring wave amplitude systematically: (1) locate rest/equilibrium (θ=0°), (2) identify maximum displacement (15° to one side), (3) measure distance (15°), (4) record as amplitude (A = 15°), and (5) verify with other side (also 15°). Amplitude in pendulums indicates swing energy (E ∝ A² approximately for small angles), and correct measurement avoids confusing with total arc.
A wave is shown on a graph with a clearly marked equilibrium line at $y=0\text{ cm}$ . The crest is at $y=+4\text{ cm}$ and the trough is at $y=-4\text{ cm}$ . Which statement correctly describes how to measure the amplitude?
Answer: Measure from the equilibrium line to the crest (or to the trough): $4\text{ cm}$ 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.
A sound wave is shown on a pressure-vs-time graph where the rest (equilibrium) pressure is atmospheric pressure. The pressure reaches a maximum of $+10\text{ Pa}$ above atmospheric and a minimum of $-10\text{ Pa}$ below atmospheric. What is the amplitude of the sound wave (maximum pressure variation from equilibrium)?
Answer: $10\text{ Pa}$ 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. For a sound wave represented as pressure variation from atmospheric pressure (rest position), amplitude is the maximum pressure deviation from equilibrium. A sound wave with rest position at atmospheric pressure, maximum pressure at +10 Pa above atmospheric (compression peak), and minimum at -10 Pa below atmospheric (rarefaction trough), has pressure amplitude A = 10 Pa: the maximum variation from equilibrium atmospheric pressure is ±10 Pa, so amplitude is 10 Pa (the maximum deviation, not the 20 Pa total range from peak to trough). Larger pressure amplitude means louder sound: 10 Pa amplitude is louder than 1 Pa amplitude (10× larger amplitude gives 10² = 100× more energy in the sound wave). Choice D is correct because it properly identifies the amplitude as 10 Pa, the maximum pressure variation from atmospheric equilibrium. Choice A incorrectly gives 20 Pa, which is the total peak-to-trough pressure range (2A), not the amplitude; Choice B suggests 0 Pa which would mean no wave at all; Choice C gives -10 Pa when amplitude is always positive magnitude (the absolute value of the maximum deviation).
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?
Answer: 5 cm 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.
Two transverse waves are measured from the same rest position ( $y=0\text{ cm}$ ). Wave A has a crest at $+2\text{ cm}$ and trough at $-2\text{ cm}$ . Wave B has a crest at $+5\text{ cm}$ and trough at $-5\text{ cm}$ . Which statement is correct?
Answer: Wave B has larger amplitude ( $5\text{ cm}$ ) than Wave A ( $2\text{ cm}$ ). 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. For comparing wave amplitudes, measure each wave's maximum displacement from the same rest position. Wave A with rest at y = 0 cm, crest at +2 cm, and trough at -2 cm has amplitude A = 2 cm (distance from 0 to +2 or from 0 to -2). Wave B with rest at y = 0 cm, crest at +5 cm, and trough at -5 cm has amplitude A = 5 cm (distance from 0 to +5 or from 0 to -5). Since 5 cm > 2 cm, Wave B has larger amplitude than Wave A, meaning Wave B carries more energy (energy ∝ A²: Wave B has (5/2)² = 6.25× more energy than Wave A). Choice C is correct because it accurately states that Wave B has larger amplitude (5 cm) than Wave A (2 cm). Choice A incorrectly claims Wave A has larger amplitude and makes the mathematical error 2 > 5; Choice B incorrectly states both have the same amplitude when they clearly differ; Choice D gives wrong values, stating Wave A has 4 cm amplitude (which would be its crest-to-trough distance) and Wave B has 10 cm amplitude (its crest-to-trough distance), confusing 2A with A.
A student measures a wave and finds the vertical distance from crest to trough is $12\text{ cm}$ . The equilibrium position is halfway between crest and trough. What is the amplitude?
Answer: $6\text{ cm}$ 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.
A water wave passes by a dock. The water level at rest (equilibrium) is flat. The highest point of the wave rises $5\text{ cm}$ above the rest level, and the lowest point dips $5\text{ cm}$ below the rest level. What is the amplitude of the wave?
Answer: $5\text{ cm}$ 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 flat calm surface, rising to 5 cm above (crest) means amplitude is 5 cm from rest to crest. The dip to 5 cm below (trough) is also 5 cm from rest (magnitude), confirming amplitude is 5 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 (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 rest level to the crest (5 cm) or trough (5 cm). Choice A measures crest to trough (10 cm) calling it amplitude when that's 2A; Choice C halves incorrectly to 2.5 cm; Choice D uses negative (-5 cm) when amplitude is positive. Measuring wave amplitude systematically: (1) locate rest/equilibrium position (flat water level), (2) identify maximum displacement point (crest 5 cm above), (3) measure distance (5 cm), (4) record as amplitude (A = 5 cm), and (5) verify with trough (also 5 cm). Larger amplitude means taller wave: 5 cm amplitude is taller than 2 cm, carrying more energy (E ∝ A², so 6.25× more), and correct measurement avoids confusing with total height.
On a displacement vs. position graph, the equilibrium line is labeled $y=0\text{ cm}$ . Each grid square represents $1\text{ cm}$ vertically. A crest is 4 squares above the equilibrium line. What is the amplitude?
Answer: $4\text{ cm}$ 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.
A wave is drawn on a graph where the vertical axis is labeled in centimeters. The equilibrium line is at $y=1\text{ cm}$ . A crest is at $y=5\text{ cm}$ and a trough is at $y=-3\text{ cm}$ . What is the amplitude of the wave?
Answer: $4\text{ cm}$ 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.
A wave is shown on a displacement graph. The rest position is the horizontal center line at $y=0\text{ m}$ . The trough reaches $y=-2\text{ m}$ . What is the amplitude?
Answer: 2 m 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 the graph, rest is at y=0 m, the trough is at y=-2 m (maximum negative displacement), so amplitude is the magnitude from rest to trough (2 m)—even without crest specified, the max displacement given is 2 m. A common mistake is using the negative value directly or assuming total height without data, or thinking no amplitude if crest not mentioned. Choice A is correct because it measures the magnitude of the maximum displacement from rest (y=0) to trough (y=-2 m), which is 2 m, properly using positive value. Choice B uses negative (-2 m) when amplitude is positive; Choice C doubles to 4 m assuming symmetry without evidence; Choice D assumes 0 m, ignoring the displacement. Measuring wave amplitude systematically: (1) locate rest (y=0), (2) identify max displacement (trough at -2 m), (3) measure magnitude (2 m), (4) record A=2 m, and (5) note if asymmetric, but max is 2 m. Amplitude significance: 2 m indicates wave strength and energy (E ∝ A²), relevant for contexts like seismic waves where trough displacement shows intensity.
A pendulum swings back and forth. Its equilibrium position is straight down at $\theta=0^\circ$ . The pendulum reaches a maximum angle of $15^\circ$ to the left and $15^\circ$ to the right. What is the amplitude of the pendulum's motion?
Answer: 15° 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.
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?
Answer: 6 cm 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.
Two sound waves are measured relative to atmospheric pressure (the equilibrium line). Wave 1 varies by $\pm 2\text{ Pa}$ , and Wave 2 varies by $\pm 6\text{ Pa}$ . Which statement is correct about amplitude and energy?
Answer: Wave 2 has larger amplitude and therefore more energy. 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. For sound waves, larger amplitude means more energy and louder sound. Wave 1 with pressure variation ±2 Pa has amplitude A₁ = 2 Pa (maximum deviation from atmospheric pressure). Wave 2 with pressure variation ±6 Pa has amplitude A₂ = 6 Pa. Since 6 Pa > 2 Pa, Wave 2 has larger amplitude than Wave 1. Energy in a wave is proportional to amplitude squared (E ∝ A²), so Wave 2 has (6/2)² = 9× more energy than Wave 1, making it significantly louder. Choice B is correct because it accurately states that Wave 2 has larger amplitude and therefore more energy. Choice A incorrectly claims Wave 1 has larger amplitude; Choice C incorrectly suggests both have the same amplitude when they clearly differ (2 Pa vs 6 Pa); Choice D incorrectly states amplitude depends only on frequency, when amplitude and frequency are independent properties of waves.
On a displacement graph, the wave's maximum displacement is $-4\text{ cm}$ (the lowest trough) and the equilibrium line is at $0\text{ cm}$ . What is the amplitude of the wave?
Answer: $4\text{ cm}$ 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.
A transverse wave is drawn on a graph. The equilibrium (rest) position is the horizontal line at $y=0\text{ cm}$ . The crest reaches $y=+3\text{ cm}$ and the trough reaches $y=-3\text{ cm}$ . What is the amplitude of the wave?
Answer: $3\text{ cm}$ 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.
A displacement graph has the rest position labeled at $y=0\text{ m}$ . The trough reaches $y=-0.7\text{ m}$ . What is the amplitude of the wave?
Answer: $0.7\text{ m}$ 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: trough at y=-0.7 m from y=0 gives A=0.7 m (magnitude). Assuming typical symmetry, the max displacement is 0.7 m, measured as positive distance from rest to trough. Choice A is correct because it takes the positive magnitude of the maximum displacement (0.7 m) from equilibrium. Choice B keeps negative sign; Choice C doubles to hypothetical 2A; Choice D halves incorrectly. Measuring wave amplitude systematically: (1) locate rest (y=0 m), (2) identify max point (trough -0.7 m), (3) take magnitude (0.7 m), (4) record A=0.7 m, and (5) note if asymmetric, but here it's given as trough only. Amplitude is always positive, preventing errors like using signed values or assuming unstated crests.

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