MYP · 09 · extended response
Reconstructing a travelling wave and an overlapping pulse
Waves · Original GioPhysics question with a detailed, mark-by-mark answer guide.
- Demand
- discriminating
- Marks
- 6
- Topics
- 2
- Answer
- Complete
Wave snapshot
Supplied question data. Read the labelled axes and use the observations to test the physical model.
Vertical axis (y): Displacement / cm
Horizontal axis (x): Position / m
Read the exact data as a table
| Position / m | Displacement / cm |
|---|---|
| 0 | 0 |
| 0.025 | 0.5853 |
| 0.05 | 1.1481 |
| 0.075 | 1.6667 |
| 0.1 | 2.1213 |
| 0.125 | 2.4944 |
| 0.15 | 2.7716 |
| 0.175 | 2.9424 |
| 0.2 | 3 |
| 0.225 | 2.9424 |
| 0.25 | 2.7716 |
| 0.275 | 2.4944 |
| 0.3 | 2.1213 |
| 0.325 | 1.6667 |
| 0.35 | 1.1481 |
| 0.375 | 0.5853 |
| 0.4 | 0 |
| 0.425 | -0.5853 |
| 0.45 | -1.1481 |
| 0.475 | -1.6667 |
| 0.5 | -2.1213 |
| 0.525 | -2.4944 |
| 0.55 | -2.7716 |
| 0.575 | -2.9424 |
| 0.6 | -3 |
| 0.625 | -2.9424 |
| 0.65 | -2.7716 |
| 0.675 | -2.4944 |
| 0.7 | -2.1213 |
| 0.725 | -1.6667 |
| 0.75 | -1.1481 |
| 0.775 | -0.5853 |
| 0.8 | 0 |
These are the supplied values, not a worked answer. Lines join the supplied values; they are not a fitted model.
Optional enrichment: this challenge may extend beyond the usual syllabus depth and assumes confidence with algebra and graph interpretation. At one instant a transverse wave has the supplied displacement–position profile. Adjacent points are joined smoothly as a sinusoid. A fixed sensor observes five complete cycles in 2.0 s. Later an upward 3.0 cm pulse and a downward 2.0 cm pulse overlap at the sensor in a linear medium. Supplied data (Position / m; Displacement / cm): (0, 0), (0.025, 0.5853), (0.05, 1.1481), (0.075, 1.6667), (0.1, 2.1213), (0.125, 2.4944), (0.15, 2.7716), (0.175, 2.9424), (0.2, 3), (0.225, 2.9424), (0.25, 2.7716), (0.275, 2.4944), (0.3, 2.1213), (0.325, 1.6667), (0.35, 1.1481), (0.375, 0.5853), (0.4, 0), (0.425, -0.5853), (0.45, -1.1481), (0.475, -1.6667), (0.5, -2.1213), (0.525, -2.4944), (0.55, -2.7716), (0.575, -2.9424), (0.6, -3), (0.625, -2.9424), (0.65, -2.7716), (0.675, -2.4944), (0.7, -2.1213), (0.725, -1.6667), (0.75, -1.1481), (0.775, -0.5853), (0.8, 0).
- (a)
Find amplitude, wavelength, period, frequency and propagation speed. Explain why the snapshot does not determine the direction of travel.
3 marks - (b)
Find the displacement during pulse overlap and explain what happens to the pulses and their transported energy afterward.
3 marks
Ready to self-mark?Reveal the detailed answer guide
(a)
Find amplitude, wavelength, period, frequency and propagation speed. Explain why the snapshot does not determine the direction of travel.
Build a chain of claim, evidence and physics reasoning. Address more than one relevant factor, identify a limitation or assumption, and finish with a conclusion that is conditional on the evidence rather than absolute.
- 1
One complete spatial cycle spans 0.80 m, and maximum displacement from equilibrium is 3.0 cm.
- 2
Frequency is cycles/time = 5/2.0 = 2.5 Hz; T = 1/f = 0.40 s; propagation speed is fλ = 2.0 m s⁻¹.
- 3
A single spatial profile can move either left or right. A later snapshot or local displacement–time information is needed to establish direction.
(b)
Find the displacement during pulse overlap and explain what happens to the pulses and their transported energy afterward.
Build a chain of claim, evidence and physics reasoning. Address more than one relevant factor, identify a limitation or assumption, and finish with a conclusion that is conditional on the evidence rather than absolute.
- 1
Superposition adds signed displacements: +3.0+(−2.0) = +1.0 cm upward.
- 2
Partial cancellation describes displacement at that location and instant. It does not mean the waves permanently destroy each other.
- 3
The pulses continue in the ideal linear model. Energy is redistributed between kinetic and elastic forms; displacement alone is insufficient to determine all local energy during overlap.
Complete marking guidance
Use these worked steps alongside the part-by-part answers. They explain the method and mark allocation; they do not add extra marks.
- One complete spatial cycle spans 0.80 m, and maximum displacement from equilibrium is 3.0 cm.
- Frequency is cycles/time = 5/2.0 = 2.5 Hz; T = 1/f = 0.40 s; propagation speed is fλ = 2.0 m s⁻¹.
- A single spatial profile can move either left or right. A later snapshot or local displacement–time information is needed to establish direction.
- Superposition adds signed displacements: +3.0+(−2.0) = +1.0 cm upward.
- Partial cancellation describes displacement at that location and instant. It does not mean the waves permanently destroy each other.
- The pulses continue in the ideal linear model. Energy is redistributed between kinetic and elastic forms; displacement alone is insufficient to determine all local energy during overlap.
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