Measure Wave Amplitude - Middle School Physical Science

1. State the formula for amplitude using maximum and minimum displacement values $y_{max}$ and $y_{min}$.

   $A = \frac{y_{max}-y_{min}}{2}$. Half the total vertical range gives the amplitude.

2. Choose the correct statement: amplitude measures wave height or the horizontal distance between crests?

   Amplitude measures wave height (vertical displacement). Wavelength measures horizontal distance; amplitude is vertical.

3. Identify what amplitude represents for a longitudinal wave (such as a sound wave).

   Maximum change in compression/rarefaction from normal. Measures pressure variation from normal atmospheric pressure.

4. What is the amplitude of a transverse wave measured from on a graph?

   From the midline to a crest or to a trough. The vertical distance from the center line to the peak or valley.

5. Which change increases amplitude: moving crests farther from the midline or moving crests closer to the midline?

   Moving crests farther from the midline. Larger amplitude means greater displacement from equilibrium.

6. What is the amplitude if a wave ranges from $-1\ \text{cm}$ to $7\ \text{cm}$ in displacement?

   $4\ \text{cm}$. Midline at $3\ \text{cm}$; amplitude is $\frac{7-(-1)}{2} = 4\ \text{cm}$.

7. Identify the amplitude on a graph of displacement vs. position: which vertical measurement is amplitude?

   Midline to crest (or midline to trough). Amplitude is the vertical distance from the center line to a peak.

8. What is wave amplitude in terms of the equilibrium (rest) position?

   Maximum displacement from the equilibrium position. Amplitude measures how far the wave moves from its rest position.

9. Identify the amplitude if a crest is at $y=+5\ \text{cm}$ and a trough is at $y=-1\ \text{cm}$.

   $3\ \text{cm}$. Find midline at $y=2$, then distance to crest is $3\ \text{cm}$.

10. Identify the amplitude if the distance from crest to trough is $12\ \text{cm}$.

    $6\ \text{cm}$. Crest-to-trough is twice the amplitude, so divide by 2.

11. Find the amplitude if a crest is at $+6\ \text{mm}$ and a trough is at $-2\ \text{mm}$.

    $4\ \text{mm}$. Use $A = \frac{6-(-2)}{2} = \frac{8}{2} = 4\ \text{mm}$.

12. Find the amplitude if the midline is $0\ \text{cm}$ and a crest is at $+3\ \text{cm}$.

    $3\ \text{cm}$. Distance from midline (0) to crest (+3) is 3 cm.

13. What is the amplitude if the midline is at $3\ \text{cm}$ and the crest is at $11\ \text{cm}$?

    $8\ \text{cm}$. Subtract midline from crest: $11 - 3 = 8\ \text{cm}$.

14. What is the amplitude if the maximum displacement is $+4\ \text{cm}$ from equilibrium?

    $4\ \text{cm}$. Amplitude equals the maximum distance from equilibrium.

15. Find the midline $y_{eq}$ if a crest is at $10\ \text{cm}$ and a trough is at $2\ \text{cm}$.

    $y_{eq}=6\ \text{cm}$. Midline is the average: $(10+2)/2 = 6$ cm.

16. What is the amplitude if the midline is $y=0$ and a crest is at $y=+3\ \text{cm}$?

    $3\ \text{cm}$. Subtract midline position from crest position to find amplitude.

17. Identify the amplitude on a displacement-time graph: is it the maximum vertical displacement or the period?

    The maximum vertical displacement. Period is horizontal time; amplitude is vertical displacement.

18. What is the relationship between amplitude and crest-to-trough height?

    Amplitude is half the crest-to-trough height. The full vertical distance is divided by 2 to get amplitude.

19. What is the amplitude if the midline is $y=2\ \text{cm}$ and a crest is at $y=8\ \text{cm}$?

    $6\ \text{cm}$. Find the difference between crest and midline positions.

20. Identify the amplitude for the wave with midline $y=0$ and peaks at $y=\pm 5$.

    $5$ (in the graph's y-units). Distance from midline (0) to peak (5) is the amplitude.

21. What is the amplitude if the midline is $5\ \text{mm}$ and the crest is $2\ \text{mm}$?

    $3\ \text{mm}$. Distance from midline to crest: $|5 - 2| = 3\ \text{mm}$.

22. Which statement best describes amplitude on a displacement-versus-position graph?

    Amplitude is the vertical distance from midline to a crest (or trough). On graphs, amplitude is measured vertically from center to peak.

23. Find the amplitude if a wave's maximum displacement is $0.25\ \text{m}$ and minimum is $-0.15\ \text{m}$.

    $A = 0.20\ \text{m}$. Use $A = \frac{0.25-(-0.15)}{2} = \frac{0.40}{2} = 0.20\ \text{m}$.

24. Which option is a correct unit for amplitude: meters, seconds, or hertz?

    Meters (or any length unit). Amplitude is a distance measurement, so uses length units.

25. Which statement correctly compares amplitude and wavelength on a wave diagram?

    Amplitude is vertical; wavelength is horizontal. Amplitude measures height; wavelength measures length.

26. What is the amplitude if the wave height is $18\ \text{cm}$?

    $9\ \text{cm}$. Wave height is twice the amplitude, so divide by 2.

27. What is the amplitude if the crest-to-trough vertical distance is $18\ \text{m}$?

    $9\ \text{m}$. Amplitude is half the crest-to-trough distance: $\frac{18}{2} = 9$.

28. What happens to amplitude if the wave height changes from $10\ \text{cm}$ to $16\ \text{cm}$?

    Amplitude increases from $5\ \text{cm}$ to $8\ \text{cm}$. New amplitude is half the new wave height.

29. State the formula for the midline (equilibrium) value using $y_{max}$ and $y_{min}$.

    $y_{mid} = \frac{y_{max}+y_{min}}{2}$. The midline is the average of maximum and minimum values.

30. What is the amplitude on a longitudinal wave diagram (compression/rarefaction) described as?

    Maximum particle displacement from rest. In longitudinal waves, particles move back and forth from equilibrium.

31. Find and correct the mistake: "Amplitude is the distance from crest to crest."

    Correct: Amplitude is midline-to-crest (or midline-to-trough). Crest-to-crest measures wavelength, not amplitude.

32. What does amplitude correspond to for a light wave in terms of what you observe?

    Brightness or intensity (greater amplitude means brighter light). Higher amplitude light waves appear brighter.

33. What does amplitude correspond to for a sound wave in terms of what you hear?

    Loudness (greater amplitude means louder sound). Higher amplitude sound waves create louder sounds.

34. Find the amplitude if the midline is at $y=2\ \text{m}$ and the crest is at $y=9\ \text{m}$.

    $7\ \text{m}$. Distance from midline (2) to crest (9) is 7 m.

35. What is the amplitude if the maximum displacement is $0.25\ \text{m}$?

    $0.25\ \text{m}$. Maximum displacement directly equals amplitude.

36. Identify the amplitude given maximum $y=5$ and minimum $y=-1$ on a wave graph.

    $A = 3$. Use $A = \frac{5-(-1)}{2} = \frac{6}{2} = 3$.

37. What is the relationship between amplitude and crest-to-trough height?

    Amplitude is half the crest-to-trough height. Total vertical distance divided by 2 gives the amplitude.

38. Find the amplitude if the crest-to-trough height is $18\ \text{cm}$.

    $9\ \text{cm}$. Divide crest-to-trough height by 2 to find amplitude.

39. Find the crest-to-trough height $H$ if the amplitude is $A = 7\ \text{m}$.

    $H = 14\ \text{m}$. Crest-to-trough height equals twice the amplitude: $H = 2A$.

40. Find the amplitude if the maximum displacement is $12\ \text{cm}$ from the midline.

    $12\ \text{cm}$. Amplitude equals the maximum displacement given.

41. What is wave amplitude in terms of the equilibrium (rest) position?

    Maximum displacement from equilibrium. Amplitude measures how far particles move from their resting position.

42. What is the amplitude if the midline is $y=2$ and the crest is at $y=9$ on a graph?

    $7$. Subtract midline value from crest value: $9 - 2 = 7$.

43. Find and correct the statement: "Amplitude is the distance from crest to trough."

    Correct: amplitude is half the crest-to-trough distance. Common error: amplitude is not the full peak-to-peak distance.

44. What does a larger amplitude usually indicate about a mechanical wave?

    More energy carried by the wave. Energy is proportional to amplitude squared.

45. Which change increases the amplitude of a wave on a graph: taller peaks or closer peaks?

    Taller peaks (greater vertical displacement). Greater vertical displacement means larger amplitude.

46. Find the amplitude if the crest-to-trough height is $14\ \text{cm}$.

    $7\ \text{cm}$. Amplitude is half the total vertical distance.

47. Which units should amplitude have if the wave displacement axis is labeled in meters?

    Meters ($\text{m}$). Amplitude has the same units as the displacement it measures.

48. What is the amplitude on a transverse wave diagram: crest height above the midline or crest-to-trough distance?

    Crest height above the midline. Amplitude is measured from midline to peak, not the full peak-to-valley distance.

49. Identify the amplitude if a trough is $7\ \text{cm}$ below the equilibrium line.

    $7\ \text{cm}$. Distance from equilibrium to trough also equals amplitude.

50. Find the amplitude if the peak-to-peak height is $14\,\text{m}$.

    $7\,\text{m}$. Peak-to-peak divided by 2: $\frac{14}{2}=7$ m.

51. Which option correctly describes amplitude: midline-to-crest or crest-to-crest distance?

    Midline-to-crest distance. Crest-to-crest is wavelength, not amplitude.

52. Identify the amplitude if the highest point is $+5\ \text{cm}$ and the lowest point is $-9\ \text{cm}$.

    $7\ \text{cm}$. Use $A = \frac{5-(-9)}{2} = \frac{14}{2} = 7\ \text{cm}$.

53. What is wave amplitude in terms of the rest (equilibrium) position?

    Maximum displacement from the rest position. Amplitude measures how far the wave moves from its center line.

54. What is the amplitude of a transverse wave measured from on a graph?

    From the midline to a crest or from the midline to a trough. Amplitude is the vertical distance from the center line to a peak.

55. Which measurement equals amplitude on a transverse wave: crest-to-rest or crest-to-trough?

    Crest-to-rest distance. Amplitude is half the crest-to-trough distance, not the full distance.

56. What SI unit is commonly used to report amplitude for water or rope waves?

    Meters (m). SI base unit for length measurements.

57. What is the amplitude if crest-to-trough distance is $0.40\ \text{m}$?

    $0.20\ \text{m}$. Crest-to-trough distance divided by 2 gives amplitude.

58. Identify the midline value if the crest is $+9\,\text{cm}$ and the trough is $-3\,\text{cm}$.

    $3\,\text{cm}$. Midline is the average: $\frac{9+(-3)}{2}=3$ cm.

59. Identify the amplitude if the maximum displacement is between $y=+10\ \text{mm}$ and $y=-10\ \text{mm}$.

    $10\ \text{mm}$. Maximum displacement from $y=0$ is the amplitude value.

60. Find and correct the statement: "Amplitude is the distance from crest to trough."

    Correct: Amplitude is half the crest-to-trough distance. The error was stating full crest-to-trough distance instead of half.

61. What is the amplitude if the midline is $y=-1\ \text{cm}$ and a trough is at $y=-5\ \text{cm}$?

    $4\ \text{cm}$. Take absolute value of trough minus midline positions.

62. Identify the amplitude if a wave ranges from $2\ \text{cm}$ to $10\ \text{cm}$ in displacement.

    $4\ \text{cm}$. Midline at $6\ \text{cm}$; amplitude is $\frac{10-2}{2} = 4\ \text{cm}$.

63. What is wave amplitude on a graph, measured from the equilibrium (midline)?

    Maximum displacement from equilibrium to a crest or trough. Amplitude measures how far the wave moves from its resting position.

64. What is the amplitude if the displacement ranges from $-6\ \text{mm}$ to $+6\ \text{mm}$?

    $6\ \text{mm}$. The amplitude is the maximum value from zero, regardless of sign.

65. Which wave has greater amplitude: $A_1=3\,\text{cm}$ or $A_2=5\,\text{cm}$?

    $A_2=5\,\text{cm}$. Compare magnitudes: 5 cm > 3 cm.

66. What is the amplitude formula using crest and trough heights on the same graph?

    $A = \frac{\text{crest} - \text{trough}}{2}$. Half the vertical distance between highest and lowest points.

67. Which graph feature represents the equilibrium position of a wave?

    The midline (average value) of the wave. The midline is the horizontal line through the wave's center.

68. Find the amplitude if the crest is at $+10\,\text{cm}$ and the trough is at $-2\,\text{cm}$.

    $6\,\text{cm}$. Midline at $\frac{10+(-2)}{2}=4$; amplitude is $10-4=6$ cm.

69. Find the amplitude if the wave ranges from $y=3\,\text{cm}$ to $y=11\,\text{cm}$.

    $4\,\text{cm}$. Midline at $\frac{3+11}{2}=7$; amplitude is $11-7=4$ cm.

70. State the formula for amplitude using peak-to-peak (crest-to-trough) distance $H$.

    $A = \frac{H}{2}$. Peak-to-peak distance divided by 2 gives the amplitude.

71. What is the relationship between wave height and amplitude?

    Wave height $= 2A$ (so amplitude $A = \frac{\text{height}}{2}$). Height spans from crest to trough, so amplitude is half that distance.

72. Find and correct the error: "Amplitude is the distance from crest to trough."

    Correct: Amplitude is half the crest-to-trough distance. The error confuses full height with amplitude.

73. Which wave property is directly related to the energy carried by a wave in most models?

    Amplitude. Higher amplitude waves carry more energy.

74. What are the typical units of amplitude on a displacement-versus-position graph?

    Units of displacement (for example, $\text{m}$ or $\text{cm}$). Amplitude shares the same units as the displacement axis.

75. Identify the amplitude if a crest is $4\ \text{mm}$ above the equilibrium line.

    $4\ \text{mm}$. Distance from equilibrium to crest equals amplitude.

76. Choose the word that best describes what larger amplitude means for a wave.

    Greater maximum displacement from equilibrium. Higher amplitude means particles move farther from rest.

77. Which measurement gives amplitude: crest-to-crest, trough-to-trough, or midline-to-crest?

    Midline-to-crest (or midline-to-trough). Amplitude is always measured from the center line to a peak.

78. Identify the amplitude if the crest is at $+6\,\text{cm}$ and the midline is $0\,\text{cm}$.

    $6\,\text{cm}$. Distance from midline (0) to crest (+6) is 6 cm.

79. Find the amplitude if the highest point is $10\ \text{cm}$ and the lowest point is $2\ \text{cm}$.

    $4\ \text{cm}$. Half the distance from highest to lowest: $(10-2)/2 = 4$ cm.

80. Which option correctly describes amplitude for a longitudinal wave (sound) on a compression diagram?

    Maximum density/pressure change from the normal (rest) level. In longitudinal waves, amplitude is the maximum compression or rarefaction.

81. Which option correctly describes amplitude on a wave diagram with a labeled midline?

    Vertical distance from the midline to a crest (or to a trough). Amplitude is measured perpendicular from midline to peak.

82. Which option describes amplitude on a longitudinal wave diagram with compressions and rarefactions?

    Maximum particle displacement from equilibrium. Even in longitudinal waves, amplitude shows displacement size.

83. What is the relationship between amplitude $A$ and crest-to-trough height $H$?

    $A = \frac{H}{2}$. Crest-to-trough height is twice the amplitude.

84. Which units are used for amplitude on a displacement graph?

    The same units as displacement (often meters). Amplitude shares the same units as the quantity being displaced.

85. Identify the amplitude if the midline is $0\ \text{cm}$ and the crest is at $+4\ \text{cm}$.

    $4\ \text{cm}$. Distance from midline ($0$) to crest ($+4$) is $4\ \text{cm}$.

86. What is the amplitude if the midline is $y=-3$ and the trough is at $y=-11$?

    $8$. Distance from midline to trough: $|-3 - (-11)| = 8$.

87. Identify the amplitude if the midline is $0\ \text{cm}$ and the trough is at $-7\ \text{cm}$.

    $7\ \text{cm}$. Distance from midline ($0$) to trough ($-7$) is $7\ \text{cm}$.

88. What is wave amplitude in terms of the equilibrium (rest) position?

    Maximum displacement from the equilibrium position. Amplitude measures how far the wave moves from its rest position.

89. Find the amplitude if the crest is $+6\ \text{mm}$ and the trough is $-2\ \text{mm}$.

    $4\ \text{mm}$. Midline at $(6+(-2))/2 = 2$, so amplitude is $6-2 = 4$ mm.

90. What is the amplitude if the midline is at $-2\ \text{cm}$ and the trough is at $-10\ \text{cm}$?

    $8\ \text{cm}$. Distance from midline to trough: $|-2 - (-10)| = 8\ \text{cm}$.

91. Find the amplitude if the midline is $2\,\text{m}$ and the crest is at $7\,\text{m}$.

    $5\,\text{m}$. Amplitude is crest minus midline: $7-2=5$ m.

92. Identify the amplitude if the trough is at $-8\,\text{mm}$ and the midline is $0\,\text{mm}$.

    $8\,\text{mm}$. Distance from midline (0) to trough (-8) is 8 mm.

93. Find the amplitude if the midline is $0\ \text{m}$ and a trough is at $-0.8\ \text{m}$.

    $0.8\ \text{m}$. Distance from midline (0) to trough (-0.8) is 0.8 m.

94. What is the amplitude if the crest-to-trough vertical distance is $0.50\ \text{m}$?

    $0.25\ \text{m}$. Half of $0.50\ \text{m}$ gives amplitude of $0.25\ \text{m}$.

95. What is the amplitude if the crest is $12\ \text{cm}$ above equilibrium and the trough is $12\ \text{cm}$ below?

    $12\ \text{cm}$. When crest and trough are equal distances from equilibrium.

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