IB · PHYSICS SL

Physics: Standard Level

Wave behaviour — Theme C

Name: ____________________Date: October 10, 2026

1.
A wave has frequency 500 Hz and travels at 340 m/s through air. Calculate its wavelength.
[3 marks]
Answer explanation
Draft walkthroughs are based on marking guidance, not independently verified derivations.
1. List the given quantities and the requested unknown. Choose the relation that connects them, state any required assumptions, then substitute before rounding. Preserve exact expressions when the task asks for an exact result.
2. Work through this mathematical step: Uses v = fλ. Write the intermediate operation, keep the units consistent where applicable, and check the relation against the quantities given in the question.
3. Work through this mathematical step: Rearranges to λ = v/f. Write the intermediate operation, keep the units consistent where applicable, and check the relation against the quantities given in the question.
4. Work through this mathematical step: Obtains λ = 0.68 m. Write the intermediate operation, keep the units consistent where applicable, and check the relation against the quantities given in the question.
5. Check the complete task again, including restrictions, units, precision and supporting evidence when relevant. Specific caution: The wave equation v = fλ applies to all wave types, though the value of v differs for each medium and wave type.
Marking points
- Uses v = fλ.
- Rearranges to λ = v/f.
- Obtains λ = 0.68 m.
Examiner tip: The wave equation v = fλ applies to all wave types, though the value of v differs for each medium and wave type.
2.
Marking analysis: A learner attempts the following task: “A wave has frequency 500 Hz and travels at 340 m/s through air. Calculate its wavelength.” Their response addresses only this point: “Uses v = fλ.” Evaluate the response against the complete 3-mark task. Identify what earns credit and state every additional requirement needed for full marks.
[3 marks]
Answer explanation
Draft walkthroughs are based on marking guidance, not independently verified derivations.
1. Separate the learner's stated response from the complete task. Credit only what their response demonstrates, then identify each missing requirement; do not assume unstated working.
2. Requirement 1: Recognises credit for the stated point: Uses v = fλ. Compare this requirement with the supplied learner response; missing evidence cannot earn credit.
3. Requirement 2: Identifies the missing requirement: Rearranges to λ = v/f. Compare this requirement with the supplied learner response; missing evidence cannot earn credit.
4. Requirement 3: Identifies the missing requirement: Obtains λ = 0.68 m. Compare this requirement with the supplied learner response; missing evidence cannot earn credit.
5. Check the complete task again, including restrictions, units, precision and supporting evidence when relevant. Specific caution: Treat each marking point as a separate requirement. Do not award the same idea twice, and do not infer work the learner did not show.
Marking points
- Recognises credit for the stated point: Uses v = fλ.
- Identifies the missing requirement: Rearranges to λ = v/f.
- Identifies the missing requirement: Obtains λ = 0.68 m.
Examiner tip: Treat each marking point as a separate requirement. Do not award the same idea twice, and do not infer work the learner did not show.
3.
Distinguish between a transverse wave and a longitudinal wave, giving one example of each.
[2 marks] · no calculator
Answer explanation
Draft walkthroughs are based on marking guidance, not independently verified derivations.
1. Break the command into its requested parts. For each part, connect a relevant fact or observation to the conclusion it supports. Describing what happens and explaining why it happens are different tasks.
2. Develop this part of the answer: States that in a transverse wave, the oscillation is perpendicular to the direction of energy transfer, e.g. light or a water wave. Show which detail or principle supports it and how it addresses the command; equivalent supported wording is acceptable.
3. Develop this part of the answer: States that in a longitudinal wave, the oscillation is parallel to the direction of energy transfer, e.g. sound. Show which detail or principle supports it and how it addresses the command; equivalent supported wording is acceptable.
4. Check the complete task again, including restrictions, units, precision and supporting evidence when relevant. Specific caution: Transverse = perpendicular (crosses the direction of travel), longitudinal = parallel (compressions and rarefactions along the direction of travel).
Marking points
- States that in a transverse wave, the oscillation is perpendicular to the direction of energy transfer, e.g. light or a water wave.
- States that in a longitudinal wave, the oscillation is parallel to the direction of energy transfer, e.g. sound.
Examiner tip: Transverse = perpendicular (crosses the direction of travel), longitudinal = parallel (compressions and rarefactions along the direction of travel).
4.
Marking analysis: A learner attempts the following task: “Distinguish between a transverse wave and a longitudinal wave, giving one example of each.” Their response addresses only this point: “States that in a transverse wave, the oscillation is perpendicular to the direction of energy transfer, e.g. light or a water wave.” Evaluate the response against the complete 2-mark task. Identify what earns credit and state every additional requirement needed for full marks.
[2 marks] · no calculator
Answer explanation
Draft walkthroughs are based on marking guidance, not independently verified derivations.
1. Separate the learner's stated response from the complete task. Credit only what their response demonstrates, then identify each missing requirement; do not assume unstated working.
2. Requirement 1: Recognises credit for the stated point: States that in a transverse wave, the oscillation is perpendicular to the direction of energy transfer, e.g. light or a water wave. Compare this requirement with the supplied learner response; missing evidence cannot earn credit.
3. Requirement 2: Identifies the missing requirement: States that in a longitudinal wave, the oscillation is parallel to the direction of energy transfer, e.g. sound. Compare this requirement with the supplied learner response; missing evidence cannot earn credit.
4. Check the complete task again, including restrictions, units, precision and supporting evidence when relevant. Specific caution: Treat each marking point as a separate requirement. Do not award the same idea twice, and do not infer work the learner did not show.
Marking points
- Recognises credit for the stated point: States that in a transverse wave, the oscillation is perpendicular to the direction of energy transfer, e.g. light or a water wave.
- Identifies the missing requirement: States that in a longitudinal wave, the oscillation is parallel to the direction of energy transfer, e.g. sound.
Examiner tip: Treat each marking point as a separate requirement. Do not award the same idea twice, and do not infer work the learner did not show.
5.
Explain the phenomenon of diffraction, and state how the amount of diffraction depends on the relationship between wavelength and gap size.
[3 marks] · no calculator
Answer explanation
Draft walkthroughs are based on marking guidance, not independently verified derivations.
1. Break the command into its requested parts. For each part, connect a relevant fact or observation to the conclusion it supports. Describing what happens and explaining why it happens are different tasks.
2. Develop this part of the answer: States that diffraction is the spreading of a wave as it passes through a gap or around an obstacle. Show which detail or principle supports it and how it addresses the command; equivalent supported wording is acceptable.
3. Develop this part of the answer: States that diffraction is most significant when the gap size is comparable to (similar in magnitude to) the wavelength. Show which detail or principle supports it and how it addresses the command; equivalent supported wording is acceptable.
4. Develop this part of the answer: States that if the gap is much larger than the wavelength, diffraction is minimal; if much smaller, little wave energy passes through at all. Show which detail or principle supports it and how it addresses the command; equivalent supported wording is acceptable.
5. Check the complete task again, including restrictions, units, precision and supporting evidence when relevant. Specific caution: Sound diffracts noticeably around doorways (wavelength comparable to gap size) while light does not (wavelength far smaller than everyday gaps) — this is why you can hear around a corner but not see around it.
Marking points
- States that diffraction is the spreading of a wave as it passes through a gap or around an obstacle.
- States that diffraction is most significant when the gap size is comparable to (similar in magnitude to) the wavelength.
- States that if the gap is much larger than the wavelength, diffraction is minimal; if much smaller, little wave energy passes through at all.
Examiner tip: Sound diffracts noticeably around doorways (wavelength comparable to gap size) while light does not (wavelength far smaller than everyday gaps) — this is why you can hear around a corner but not see around it.
6.
Marking analysis: A learner attempts the following task: “Explain the phenomenon of diffraction, and state how the amount of diffraction depends on the relationship between wavelength and gap size.” Their response addresses only this point: “States that diffraction is the spreading of a wave as it passes through a gap or around an obstacle.” Evaluate the response against the complete 3-mark task. Identify what earns credit and state every additional requirement needed for full marks.
[3 marks] · no calculator
Answer explanation
Draft walkthroughs are based on marking guidance, not independently verified derivations.
1. Separate the learner's stated response from the complete task. Credit only what their response demonstrates, then identify each missing requirement; do not assume unstated working.
2. Requirement 1: Recognises credit for the stated point: States that diffraction is the spreading of a wave as it passes through a gap or around an obstacle. Compare this requirement with the supplied learner response; missing evidence cannot earn credit.
3. Requirement 2: Identifies the missing requirement: States that diffraction is most significant when the gap size is comparable to (similar in magnitude to) the wavelength. Compare this requirement with the supplied learner response; missing evidence cannot earn credit.
4. Requirement 3: Identifies the missing requirement: States that if the gap is much larger than the wavelength, diffraction is minimal; if much smaller, little wave energy passes through at all. Compare this requirement with the supplied learner response; missing evidence cannot earn credit.
5. Check the complete task again, including restrictions, units, precision and supporting evidence when relevant. Specific caution: Treat each marking point as a separate requirement. Do not award the same idea twice, and do not infer work the learner did not show.
Marking points
- Recognises credit for the stated point: States that diffraction is the spreading of a wave as it passes through a gap or around an obstacle.
- Identifies the missing requirement: States that diffraction is most significant when the gap size is comparable to (similar in magnitude to) the wavelength.
- Identifies the missing requirement: States that if the gap is much larger than the wavelength, diffraction is minimal; if much smaller, little wave energy passes through at all.
Examiner tip: Treat each marking point as a separate requirement. Do not award the same idea twice, and do not infer work the learner did not show.
7.
Two coherent wave sources produce an interference pattern. State the condition for constructive interference and the condition for destructive interference, in terms of path difference.
[3 marks] · no calculator
Answer explanation
Draft walkthroughs are based on marking guidance, not independently verified derivations.
1. Break the command into its requested parts. For each part, connect a relevant fact or observation to the conclusion it supports. Describing what happens and explaining why it happens are different tasks.
2. Work through this mathematical step: States that constructive interference occurs when the path difference is a whole number of wavelengths (nλ, n = 0, 1, 2...). Write the intermediate operation, keep the units consistent where applicable, and check the relation against the quantities given in the question.
3. Develop this part of the answer: States that destructive interference occurs when the path difference is a whole number plus a half wavelength ((n + ½)λ). Show which detail or principle supports it and how it addresses the command; equivalent supported wording is acceptable.
4. Develop this part of the answer: States that coherent sources must have a constant phase difference and the same frequency for a stable interference pattern to form. Show which detail or principle supports it and how it addresses the command; equivalent supported wording is acceptable.
5. Check the complete task again, including restrictions, units, precision and supporting evidence when relevant. Specific caution: Coherence (constant phase relationship, same frequency) is a prerequisite for observing a stable interference pattern at all — without it, the pattern shifts too fast to see.
Marking points
- States that constructive interference occurs when the path difference is a whole number of wavelengths (nλ, n = 0, 1, 2...).
- States that destructive interference occurs when the path difference is a whole number plus a half wavelength ((n + ½)λ).
- States that coherent sources must have a constant phase difference and the same frequency for a stable interference pattern to form.
Examiner tip: Coherence (constant phase relationship, same frequency) is a prerequisite for observing a stable interference pattern at all — without it, the pattern shifts too fast to see.
8.
Marking analysis: A learner attempts the following task: “Two coherent wave sources produce an interference pattern. State the condition for constructive interference and the condition for destructive interference, in terms of path difference.” Their response addresses only this point: “States that constructive interference occurs when the path difference is a whole number of wavelengths (nλ, n = 0, 1, 2...).” Evaluate the response against the complete 3-mark task. Identify what earns credit and state every additional requirement needed for full marks.
[3 marks] · no calculator
Answer explanation
Draft walkthroughs are based on marking guidance, not independently verified derivations.
1. Separate the learner's stated response from the complete task. Credit only what their response demonstrates, then identify each missing requirement; do not assume unstated working.
2. Requirement 1: Recognises credit for the stated point: States that constructive interference occurs when the path difference is a whole number of wavelengths (nλ, n = 0, 1, 2...). Compare this requirement with the supplied learner response; missing evidence cannot earn credit.
3. Requirement 2: Identifies the missing requirement: States that destructive interference occurs when the path difference is a whole number plus a half wavelength ((n + ½)λ). Compare this requirement with the supplied learner response; missing evidence cannot earn credit.
4. Requirement 3: Identifies the missing requirement: States that coherent sources must have a constant phase difference and the same frequency for a stable interference pattern to form. Compare this requirement with the supplied learner response; missing evidence cannot earn credit.
5. Check the complete task again, including restrictions, units, precision and supporting evidence when relevant. Specific caution: Treat each marking point as a separate requirement. Do not award the same idea twice, and do not infer work the learner did not show.
Marking points
- Recognises credit for the stated point: States that constructive interference occurs when the path difference is a whole number of wavelengths (nλ, n = 0, 1, 2...).
- Identifies the missing requirement: States that destructive interference occurs when the path difference is a whole number plus a half wavelength ((n + ½)λ).
- Identifies the missing requirement: States that coherent sources must have a constant phase difference and the same frequency for a stable interference pattern to form.
Examiner tip: Treat each marking point as a separate requirement. Do not award the same idea twice, and do not infer work the learner did not show.
9.
A string fixed at both ends of length 0.80 m vibrates in its fundamental (first harmonic) standing wave mode. Calculate the wavelength of this standing wave.
[3 marks]
Answer explanation
Draft walkthroughs are based on marking guidance, not independently verified derivations.
1. List the given quantities and the requested unknown. Choose the relation that connects them, state any required assumptions, then substitute before rounding. Preserve exact expressions when the task asks for an exact result.
2. Develop this part of the answer: States that the fundamental mode of a string fixed at both ends has a node at each end and one antinode in the middle, so the string length equals half a wavelength. Show which detail or principle supports it and how it addresses the command; equivalent supported wording is acceptable.
3. Work through this mathematical step: Uses L = λ/2. Write the intermediate operation, keep the units consistent where applicable, and check the relation against the quantities given in the question.
4. Work through this mathematical step: Obtains λ = 1.6 m. Write the intermediate operation, keep the units consistent where applicable, and check the relation against the quantities given in the question.
5. Check the complete task again, including restrictions, units, precision and supporting evidence when relevant. Specific caution: For a string fixed at both ends, the fundamental wavelength is always twice the string length — a relationship worth memorising directly.
Marking points
- States that the fundamental mode of a string fixed at both ends has a node at each end and one antinode in the middle, so the string length equals half a wavelength.
- Uses L = λ/2.
- Obtains λ = 1.6 m.
Examiner tip: For a string fixed at both ends, the fundamental wavelength is always twice the string length — a relationship worth memorising directly.
10.
Marking analysis: A learner attempts the following task: “A string fixed at both ends of length 0.80 m vibrates in its fundamental (first harmonic) standing wave mode. Calculate the wavelength of this standing wave.” Their response addresses only this point: “States that the fundamental mode of a string fixed at both ends has a node at each end and one antinode in the middle, so the string length equals half a wavelength.” Evaluate the response against the complete 3-mark task. Identify what earns credit and state every additional requirement needed for full marks.
[3 marks]
Answer explanation
Draft walkthroughs are based on marking guidance, not independently verified derivations.
1. Separate the learner's stated response from the complete task. Credit only what their response demonstrates, then identify each missing requirement; do not assume unstated working.
2. Requirement 1: Recognises credit for the stated point: States that the fundamental mode of a string fixed at both ends has a node at each end and one antinode in the middle, so the string length equals half a wavelength. Compare this requirement with the supplied learner response; missing evidence cannot earn credit.
3. Requirement 2: Identifies the missing requirement: Uses L = λ/2. Compare this requirement with the supplied learner response; missing evidence cannot earn credit.
4. Requirement 3: Identifies the missing requirement: Obtains λ = 1.6 m. Compare this requirement with the supplied learner response; missing evidence cannot earn credit.
5. Check the complete task again, including restrictions, units, precision and supporting evidence when relevant. Specific caution: Treat each marking point as a separate requirement. Do not award the same idea twice, and do not infer work the learner did not show.
Marking points
- Recognises credit for the stated point: States that the fundamental mode of a string fixed at both ends has a node at each end and one antinode in the middle, so the string length equals half a wavelength.
- Identifies the missing requirement: Uses L = λ/2.
- Identifies the missing requirement: Obtains λ = 1.6 m.
Examiner tip: Treat each marking point as a separate requirement. Do not award the same idea twice, and do not infer work the learner did not show.
11.
Distinguish between a standing (stationary) wave and a travelling wave, in terms of energy transfer.
[2 marks] · no calculator
Answer explanation
Draft walkthroughs are based on marking guidance, not independently verified derivations.
1. Break the command into its requested parts. For each part, connect a relevant fact or observation to the conclusion it supports. Describing what happens and explaining why it happens are different tasks.
2. Develop this part of the answer: States that a travelling wave transfers energy from one place to another. Show which detail or principle supports it and how it addresses the command; equivalent supported wording is acceptable.
3. Develop this part of the answer: States that a standing wave stores energy locally, oscillating between kinetic and potential forms, with no net energy transfer along its length. Show which detail or principle supports it and how it addresses the command; equivalent supported wording is acceptable.
4. Check the complete task again, including restrictions, units, precision and supporting evidence when relevant. Specific caution: A standing wave forms from the superposition of two identical travelling waves moving in opposite directions — their energy transfers cancel out on average.
Marking points
- States that a travelling wave transfers energy from one place to another.
- States that a standing wave stores energy locally, oscillating between kinetic and potential forms, with no net energy transfer along its length.
Examiner tip: A standing wave forms from the superposition of two identical travelling waves moving in opposite directions — their energy transfers cancel out on average.
12.
Marking analysis: A learner attempts the following task: “Distinguish between a standing (stationary) wave and a travelling wave, in terms of energy transfer.” Their response addresses only this point: “States that a travelling wave transfers energy from one place to another.” Evaluate the response against the complete 2-mark task. Identify what earns credit and state every additional requirement needed for full marks.
[2 marks] · no calculator
Answer explanation
Draft walkthroughs are based on marking guidance, not independently verified derivations.
1. Separate the learner's stated response from the complete task. Credit only what their response demonstrates, then identify each missing requirement; do not assume unstated working.
2. Requirement 1: Recognises credit for the stated point: States that a travelling wave transfers energy from one place to another. Compare this requirement with the supplied learner response; missing evidence cannot earn credit.
3. Requirement 2: Identifies the missing requirement: States that a standing wave stores energy locally, oscillating between kinetic and potential forms, with no net energy transfer along its length. Compare this requirement with the supplied learner response; missing evidence cannot earn credit.
4. Check the complete task again, including restrictions, units, precision and supporting evidence when relevant. Specific caution: Treat each marking point as a separate requirement. Do not award the same idea twice, and do not infer work the learner did not show.
Marking points
- Recognises credit for the stated point: States that a travelling wave transfers energy from one place to another.
- Identifies the missing requirement: States that a standing wave stores energy locally, oscillating between kinetic and potential forms, with no net energy transfer along its length.
Examiner tip: Treat each marking point as a separate requirement. Do not award the same idea twice, and do not infer work the learner did not show.
13.
A wave travels from deep water into shallow water and its speed decreases. Explain what happens to its wavelength, and state what happens to its frequency.
[3 marks] · no calculator
Answer explanation
Draft walkthroughs are based on marking guidance, not independently verified derivations.
1. Break the command into its requested parts. For each part, connect a relevant fact or observation to the conclusion it supports. Describing what happens and explaining why it happens are different tasks.
2. Develop this part of the answer: States that the frequency of the wave remains unchanged, since it is set by the source generating the wave. Show which detail or principle supports it and how it addresses the command; equivalent supported wording is acceptable.
3. Work through this mathematical step: States that since v = fλ and v decreases while f stays constant, the wavelength must decrease proportionally. Write the intermediate operation, keep the units consistent where applicable, and check the relation against the quantities given in the question.
4. Develop this part of the answer: Explains that this change in wavelength as waves approach a shoreline at an angle is what causes them to bend (refract). Show which detail or principle supports it and how it addresses the command; equivalent supported wording is acceptable.
5. Check the complete task again, including restrictions, units, precision and supporting evidence when relevant. Specific caution: Frequency is always fixed by the source and never changes when a wave changes medium — only speed and wavelength change together, in the same proportion.
Marking points
- States that the frequency of the wave remains unchanged, since it is set by the source generating the wave.
- States that since v = fλ and v decreases while f stays constant, the wavelength must decrease proportionally.
- Explains that this change in wavelength as waves approach a shoreline at an angle is what causes them to bend (refract).
Examiner tip: Frequency is always fixed by the source and never changes when a wave changes medium — only speed and wavelength change together, in the same proportion.
14.
Marking analysis: A learner attempts the following task: “A wave travels from deep water into shallow water and its speed decreases. Explain what happens to its wavelength, and state what happens to its frequency.” Their response addresses only this point: “States that the frequency of the wave remains unchanged, since it is set by the source generating the wave.” Evaluate the response against the complete 3-mark task. Identify what earns credit and state every additional requirement needed for full marks.
[3 marks] · no calculator
Answer explanation
Draft walkthroughs are based on marking guidance, not independently verified derivations.
1. Separate the learner's stated response from the complete task. Credit only what their response demonstrates, then identify each missing requirement; do not assume unstated working.
2. Requirement 1: Recognises credit for the stated point: States that the frequency of the wave remains unchanged, since it is set by the source generating the wave. Compare this requirement with the supplied learner response; missing evidence cannot earn credit.
3. Requirement 2: Identifies the missing requirement: States that since v = fλ and v decreases while f stays constant, the wavelength must decrease proportionally. Compare this requirement with the supplied learner response; missing evidence cannot earn credit.
4. Requirement 3: Identifies the missing requirement: Explains that this change in wavelength as waves approach a shoreline at an angle is what causes them to bend (refract). Compare this requirement with the supplied learner response; missing evidence cannot earn credit.
5. Check the complete task again, including restrictions, units, precision and supporting evidence when relevant. Specific caution: Treat each marking point as a separate requirement. Do not award the same idea twice, and do not infer work the learner did not show.
Marking points
- Recognises credit for the stated point: States that the frequency of the wave remains unchanged, since it is set by the source generating the wave.
- Identifies the missing requirement: States that since v = fλ and v decreases while f stays constant, the wavelength must decrease proportionally.
- Identifies the missing requirement: Explains that this change in wavelength as waves approach a shoreline at an angle is what causes them to bend (refract).
Examiner tip: Treat each marking point as a separate requirement. Do not award the same idea twice, and do not infer work the learner did not show.
15.
Describe an experiment using a ripple tank to demonstrate the reflection of a plane water wave from a straight barrier, and state the relationship between the angle of incidence and the angle of reflection.
[3 marks] · no calculator
Answer explanation
Draft walkthroughs are based on marking guidance, not independently verified derivations.
1. Break the command into its requested parts. For each part, connect a relevant fact or observation to the conclusion it supports. Describing what happens and explaining why it happens are different tasks.
2. Develop this part of the answer: Describes generating plane water waves in a ripple tank using a vibrating bar, directed at a straight barrier placed in the water. Show which detail or principle supports it and how it addresses the command; equivalent supported wording is acceptable.
3. Develop this part of the answer: Describes observing the reflected wave pattern from above (e.g. using a stroboscope or by viewing shadows). Show which detail or principle supports it and how it addresses the command; equivalent supported wording is acceptable.
4. Develop this part of the answer: States that the angle of incidence equals the angle of reflection. Show which detail or principle supports it and how it addresses the command; equivalent supported wording is acceptable.
5. Check the complete task again, including restrictions, units, precision and supporting evidence when relevant. Specific caution: The law of reflection (angle of incidence = angle of reflection) applies identically to water waves, light and sound.
Marking points
- Describes generating plane water waves in a ripple tank using a vibrating bar, directed at a straight barrier placed in the water.
- Describes observing the reflected wave pattern from above (e.g. using a stroboscope or by viewing shadows).
- States that the angle of incidence equals the angle of reflection.
Examiner tip: The law of reflection (angle of incidence = angle of reflection) applies identically to water waves, light and sound.
16.
Marking analysis: A learner attempts the following task: “Describe an experiment using a ripple tank to demonstrate the reflection of a plane water wave from a straight barrier, and state the relationship between the angle of incidence and the angle of reflection.” Their response addresses only this point: “Describes generating plane water waves in a ripple tank using a vibrating bar, directed at a straight barrier placed in the water.” Evaluate the response against the complete 3-mark task. Identify what earns credit and state every additional requirement needed for full marks.
[3 marks] · no calculator
Answer explanation
Draft walkthroughs are based on marking guidance, not independently verified derivations.
1. Separate the learner's stated response from the complete task. Credit only what their response demonstrates, then identify each missing requirement; do not assume unstated working.
2. Requirement 1: Recognises credit for the stated point: Describes generating plane water waves in a ripple tank using a vibrating bar, directed at a straight barrier placed in the water. Compare this requirement with the supplied learner response; missing evidence cannot earn credit.
3. Requirement 2: Identifies the missing requirement: Describes observing the reflected wave pattern from above (e.g. using a stroboscope or by viewing shadows). Compare this requirement with the supplied learner response; missing evidence cannot earn credit.
4. Requirement 3: Identifies the missing requirement: States that the angle of incidence equals the angle of reflection. Compare this requirement with the supplied learner response; missing evidence cannot earn credit.
5. Check the complete task again, including restrictions, units, precision and supporting evidence when relevant. Specific caution: Treat each marking point as a separate requirement. Do not award the same idea twice, and do not infer work the learner did not show.
Marking points
- Recognises credit for the stated point: Describes generating plane water waves in a ripple tank using a vibrating bar, directed at a straight barrier placed in the water.
- Identifies the missing requirement: Describes observing the reflected wave pattern from above (e.g. using a stroboscope or by viewing shadows).
- Identifies the missing requirement: States that the angle of incidence equals the angle of reflection.
Examiner tip: Treat each marking point as a separate requirement. Do not award the same idea twice, and do not infer work the learner did not show.
17.
Light of wavelength 600 nm passes through a diffraction grating with 500 lines per mm. Calculate the angle of the first-order maximum, using nλ = d sinθ.
[4 marks]
Answer explanation
Draft walkthroughs are based on marking guidance, not independently verified derivations.
1. List the given quantities and the requested unknown. Choose the relation that connects them, state any required assumptions, then substitute before rounding. Preserve exact expressions when the task asks for an exact result.
2. Work through this mathematical step: Calculates the grating spacing d = 1/(500 lines/mm) = 2.0 × 10⁻⁶ m. Write the intermediate operation, keep the units consistent where applicable, and check the relation against the quantities given in the question.
3. Work through this mathematical step: Substitutes into nλ = d sinθ with n = 1, λ = 600 × 10⁻⁹ m. Write the intermediate operation, keep the units consistent where applicable, and check the relation against the quantities given in the question.
4. Work through this mathematical step: Rearranges to sinθ = λ/d = (600 × 10⁻⁹)/(2.0 × 10⁻⁶). Write the intermediate operation, keep the units consistent where applicable, and check the relation against the quantities given in the question.
5. Develop this part of the answer: Obtains θ ≈ 17.5°. Show which detail or principle supports it and how it addresses the command; equivalent supported wording is acceptable.
6. Check the complete task again, including restrictions, units, precision and supporting evidence when relevant. Specific caution: Convert 'lines per mm' to the grating spacing d in metres (d = 1/N) before substituting into the grating equation — a common early error is using N directly.
Marking points
- Calculates the grating spacing d = 1/(500 lines/mm) = 2.0 × 10⁻⁶ m.
- Substitutes into nλ = d sinθ with n = 1, λ = 600 × 10⁻⁹ m.
- Rearranges to sinθ = λ/d = (600 × 10⁻⁹)/(2.0 × 10⁻⁶).
- Obtains θ ≈ 17.5°.
Examiner tip: Convert 'lines per mm' to the grating spacing d in metres (d = 1/N) before substituting into the grating equation — a common early error is using N directly.
18.
Marking analysis: A learner attempts the following task: “Light of wavelength 600 nm passes through a diffraction grating with 500 lines per mm. Calculate the angle of the first-order maximum, using nλ = d sinθ.” Their response addresses only this point: “Calculates the grating spacing d = 1/(500 lines/mm) = 2.0 × 10⁻⁶ m.” Evaluate the response against the complete 4-mark task. Identify what earns credit and state every additional requirement needed for full marks.
[4 marks]
Answer explanation
Draft walkthroughs are based on marking guidance, not independently verified derivations.
1. Separate the learner's stated response from the complete task. Credit only what their response demonstrates, then identify each missing requirement; do not assume unstated working.
2. Requirement 1: Recognises credit for the stated point: Calculates the grating spacing d = 1/(500 lines/mm) = 2.0 × 10⁻⁶ m. Compare this requirement with the supplied learner response; missing evidence cannot earn credit.
3. Requirement 2: Identifies the missing requirement: Substitutes into nλ = d sinθ with n = 1, λ = 600 × 10⁻⁹ m. Compare this requirement with the supplied learner response; missing evidence cannot earn credit.
4. Requirement 3: Identifies the missing requirement: Rearranges to sinθ = λ/d = (600 × 10⁻⁹)/(2.0 × 10⁻⁶). Compare this requirement with the supplied learner response; missing evidence cannot earn credit.
5. Requirement 4: Identifies the missing requirement: Obtains θ ≈ 17.5°. Compare this requirement with the supplied learner response; missing evidence cannot earn credit.
6. Check the complete task again, including restrictions, units, precision and supporting evidence when relevant. Specific caution: Treat each marking point as a separate requirement. Do not award the same idea twice, and do not infer work the learner did not show.
Marking points
- Recognises credit for the stated point: Calculates the grating spacing d = 1/(500 lines/mm) = 2.0 × 10⁻⁶ m.
- Identifies the missing requirement: Substitutes into nλ = d sinθ with n = 1, λ = 600 × 10⁻⁹ m.
- Identifies the missing requirement: Rearranges to sinθ = λ/d = (600 × 10⁻⁹)/(2.0 × 10⁻⁶).
- Identifies the missing requirement: Obtains θ ≈ 17.5°.
Examiner tip: Treat each marking point as a separate requirement. Do not award the same idea twice, and do not infer work the learner did not show.
19.
A source of sound moves towards a stationary observer. Explain, using the Doppler effect, why the observer hears a higher frequency than the source emits.
[3 marks] · no calculator
Answer explanation
Draft walkthroughs are based on marking guidance, not independently verified derivations.
1. Break the command into its requested parts. For each part, connect a relevant fact or observation to the conclusion it supports. Describing what happens and explaining why it happens are different tasks.
2. Develop this part of the answer: States that as the source moves towards the observer, successive wavefronts are emitted from positions closer to the observer than the previous one. Show which detail or principle supports it and how it addresses the command; equivalent supported wording is acceptable.
3. Develop this part of the answer: States that this compresses (shortens) the wavelength of the sound reaching the observer, compared to a stationary source. Show which detail or principle supports it and how it addresses the command; equivalent supported wording is acceptable.
4. Work through this mathematical step: States that since v = fλ and the wave speed in the medium is unchanged, a shorter wavelength means the observer detects a higher frequency. Write the intermediate operation, keep the units consistent where applicable, and check the relation against the quantities given in the question.
5. Check the complete task again, including restrictions, units, precision and supporting evidence when relevant. Specific caution: The Doppler effect changes the observed wavelength and frequency, but the wave's speed in the medium itself is unaffected by the source's motion.
Marking points
- States that as the source moves towards the observer, successive wavefronts are emitted from positions closer to the observer than the previous one.
- States that this compresses (shortens) the wavelength of the sound reaching the observer, compared to a stationary source.
- States that since v = fλ and the wave speed in the medium is unchanged, a shorter wavelength means the observer detects a higher frequency.
Examiner tip: The Doppler effect changes the observed wavelength and frequency, but the wave's speed in the medium itself is unaffected by the source's motion.
20.
Marking analysis: A learner attempts the following task: “A source of sound moves towards a stationary observer. Explain, using the Doppler effect, why the observer hears a higher frequency than the source emits.” Their response addresses only this point: “States that as the source moves towards the observer, successive wavefronts are emitted from positions closer to the observer than the previous one.” Evaluate the response against the complete 3-mark task. Identify what earns credit and state every additional requirement needed for full marks.
[3 marks] · no calculator
Answer explanation
Draft walkthroughs are based on marking guidance, not independently verified derivations.
1. Separate the learner's stated response from the complete task. Credit only what their response demonstrates, then identify each missing requirement; do not assume unstated working.
2. Requirement 1: Recognises credit for the stated point: States that as the source moves towards the observer, successive wavefronts are emitted from positions closer to the observer than the previous one. Compare this requirement with the supplied learner response; missing evidence cannot earn credit.
3. Requirement 2: Identifies the missing requirement: States that this compresses (shortens) the wavelength of the sound reaching the observer, compared to a stationary source. Compare this requirement with the supplied learner response; missing evidence cannot earn credit.
4. Requirement 3: Identifies the missing requirement: States that since v = fλ and the wave speed in the medium is unchanged, a shorter wavelength means the observer detects a higher frequency. Compare this requirement with the supplied learner response; missing evidence cannot earn credit.
5. Check the complete task again, including restrictions, units, precision and supporting evidence when relevant. Specific caution: Treat each marking point as a separate requirement. Do not award the same idea twice, and do not infer work the learner did not show.
Marking points
- Recognises credit for the stated point: States that as the source moves towards the observer, successive wavefronts are emitted from positions closer to the observer than the previous one.
- Identifies the missing requirement: States that this compresses (shortens) the wavelength of the sound reaching the observer, compared to a stationary source.
- Identifies the missing requirement: States that since v = fλ and the wave speed in the medium is unchanged, a shorter wavelength means the observer detects a higher frequency.
Examiner tip: Treat each marking point as a separate requirement. Do not award the same idea twice, and do not infer work the learner did not show.
21.
In a double-slit experiment, light of wavelength 550 nm passes through two slits separated by 0.20 mm, producing an interference pattern on a screen 2.0 m away. Calculate the fringe spacing.
[4 marks]
Answer explanation
Draft walkthroughs are based on marking guidance, not independently verified derivations.
1. List the given quantities and the requested unknown. Choose the relation that connects them, state any required assumptions, then substitute before rounding. Preserve exact expressions when the task asks for an exact result.
2. Work through this mathematical step: States the fringe spacing formula: s = λD/d. Write the intermediate operation, keep the units consistent where applicable, and check the relation against the quantities given in the question.
3. Work through this mathematical step: Converts units consistently: λ = 550 × 10⁻⁹ m, d = 0.20 × 10⁻³ m, D = 2.0 m. Write the intermediate operation, keep the units consistent where applicable, and check the relation against the quantities given in the question.
4. Work through this mathematical step: Substitutes s = (550 × 10⁻⁹ × 2.0)/(0.20 × 10⁻³). Write the intermediate operation, keep the units consistent where applicable, and check the relation against the quantities given in the question.
5. Develop this part of the answer: Obtains s ≈ 5.5 × 10⁻³ m (5.5 mm). Show which detail or principle supports it and how it addresses the command; equivalent supported wording is acceptable.
6. Check the complete task again, including restrictions, units, precision and supporting evidence when relevant. Specific caution: The double-slit fringe spacing formula requires the slit separation d to be much smaller than the screen distance D, which is why d and D must be converted to the same unit (metres) with great care given their very different sizes.
Marking points
- States the fringe spacing formula: s = λD/d.
- Converts units consistently: λ = 550 × 10⁻⁹ m, d = 0.20 × 10⁻³ m, D = 2.0 m.
- Substitutes s = (550 × 10⁻⁹ × 2.0)/(0.20 × 10⁻³).
- Obtains s ≈ 5.5 × 10⁻³ m (5.5 mm).
Examiner tip: The double-slit fringe spacing formula requires the slit separation d to be much smaller than the screen distance D, which is why d and D must be converted to the same unit (metres) with great care given their very different sizes.
22.
Marking analysis: A learner attempts the following task: “In a double-slit experiment, light of wavelength 550 nm passes through two slits separated by 0.20 mm, producing an interference pattern on a screen 2.0 m away. Calculate the fringe spacing.” Their response addresses only this point: “States the fringe spacing formula: s = λD/d.” Evaluate the response against the complete 4-mark task. Identify what earns credit and state every additional requirement needed for full marks.
[4 marks]
Answer explanation
Draft walkthroughs are based on marking guidance, not independently verified derivations.
1. Separate the learner's stated response from the complete task. Credit only what their response demonstrates, then identify each missing requirement; do not assume unstated working.
2. Requirement 1: Recognises credit for the stated point: States the fringe spacing formula: s = λD/d. Compare this requirement with the supplied learner response; missing evidence cannot earn credit.
3. Requirement 2: Identifies the missing requirement: Converts units consistently: λ = 550 × 10⁻⁹ m, d = 0.20 × 10⁻³ m, D = 2.0 m. Compare this requirement with the supplied learner response; missing evidence cannot earn credit.
4. Requirement 3: Identifies the missing requirement: Substitutes s = (550 × 10⁻⁹ × 2.0)/(0.20 × 10⁻³). Compare this requirement with the supplied learner response; missing evidence cannot earn credit.
5. Requirement 4: Identifies the missing requirement: Obtains s ≈ 5.5 × 10⁻³ m (5.5 mm). Compare this requirement with the supplied learner response; missing evidence cannot earn credit.
6. Check the complete task again, including restrictions, units, precision and supporting evidence when relevant. Specific caution: Treat each marking point as a separate requirement. Do not award the same idea twice, and do not infer work the learner did not show.
Marking points
- Recognises credit for the stated point: States the fringe spacing formula: s = λD/d.
- Identifies the missing requirement: Converts units consistently: λ = 550 × 10⁻⁹ m, d = 0.20 × 10⁻³ m, D = 2.0 m.
- Identifies the missing requirement: Substitutes s = (550 × 10⁻⁹ × 2.0)/(0.20 × 10⁻³).
- Identifies the missing requirement: Obtains s ≈ 5.5 × 10⁻³ m (5.5 mm).
Examiner tip: Treat each marking point as a separate requirement. Do not award the same idea twice, and do not infer work the learner did not show.
23.
State what is meant by plane polarisation of a transverse wave, and explain why longitudinal waves, such as sound, cannot be polarised.
[3 marks] · no calculator
Answer explanation
Draft walkthroughs are based on marking guidance, not independently verified derivations.
1. Break the command into its requested parts. For each part, connect a relevant fact or observation to the conclusion it supports. Describing what happens and explaining why it happens are different tasks.
2. Develop this part of the answer: States that a plane-polarised transverse wave oscillates in only one fixed plane (direction), rather than in all directions perpendicular to the direction of travel. Show which detail or principle supports it and how it addresses the command; equivalent supported wording is acceptable.
3. Develop this part of the answer: States that longitudinal waves oscillate parallel to (along) the direction of energy transfer, not perpendicular to it. Show which detail or principle supports it and how it addresses the command; equivalent supported wording is acceptable.
4. Develop this part of the answer: States that since there is no perpendicular plane of oscillation to restrict in a longitudinal wave, polarisation, which requires restricting a transverse oscillation to one plane, is not possible. Show which detail or principle supports it and how it addresses the command; equivalent supported wording is acceptable.
5. Check the complete task again, including restrictions, units, precision and supporting evidence when relevant. Specific caution: Polarisation is unique evidence that a wave is transverse — the fact that light can be polarised (e.g. by polarising filters) is itself strong evidence for light being a transverse wave.
Marking points
- States that a plane-polarised transverse wave oscillates in only one fixed plane (direction), rather than in all directions perpendicular to the direction of travel.
- States that longitudinal waves oscillate parallel to (along) the direction of energy transfer, not perpendicular to it.
- States that since there is no perpendicular plane of oscillation to restrict in a longitudinal wave, polarisation, which requires restricting a transverse oscillation to one plane, is not possible.
Examiner tip: Polarisation is unique evidence that a wave is transverse — the fact that light can be polarised (e.g. by polarising filters) is itself strong evidence for light being a transverse wave.
24.
Marking analysis: A learner attempts the following task: “State what is meant by plane polarisation of a transverse wave, and explain why longitudinal waves, such as sound, cannot be polarised.” Their response addresses only this point: “States that a plane-polarised transverse wave oscillates in only one fixed plane (direction), rather than in all directions perpendicular to the direction of travel.” Evaluate the response against the complete 3-mark task. Identify what earns credit and state every additional requirement needed for full marks.
[3 marks] · no calculator
Answer explanation
Draft walkthroughs are based on marking guidance, not independently verified derivations.
1. Separate the learner's stated response from the complete task. Credit only what their response demonstrates, then identify each missing requirement; do not assume unstated working.
2. Requirement 1: Recognises credit for the stated point: States that a plane-polarised transverse wave oscillates in only one fixed plane (direction), rather than in all directions perpendicular to the direction of travel. Compare this requirement with the supplied learner response; missing evidence cannot earn credit.
3. Requirement 2: Identifies the missing requirement: States that longitudinal waves oscillate parallel to (along) the direction of energy transfer, not perpendicular to it. Compare this requirement with the supplied learner response; missing evidence cannot earn credit.
4. Requirement 3: Identifies the missing requirement: States that since there is no perpendicular plane of oscillation to restrict in a longitudinal wave, polarisation, which requires restricting a transverse oscillation to one plane, is not possible. Compare this requirement with the supplied learner response; missing evidence cannot earn credit.
5. Check the complete task again, including restrictions, units, precision and supporting evidence when relevant. Specific caution: Treat each marking point as a separate requirement. Do not award the same idea twice, and do not infer work the learner did not show.
Marking points
- Recognises credit for the stated point: States that a plane-polarised transverse wave oscillates in only one fixed plane (direction), rather than in all directions perpendicular to the direction of travel.
- Identifies the missing requirement: States that longitudinal waves oscillate parallel to (along) the direction of energy transfer, not perpendicular to it.
- Identifies the missing requirement: States that since there is no perpendicular plane of oscillation to restrict in a longitudinal wave, polarisation, which requires restricting a transverse oscillation to one plane, is not possible.
Examiner tip: Treat each marking point as a separate requirement. Do not award the same idea twice, and do not infer work the learner did not show.
25.
A ray of light travels from air into a glass block, with an angle of incidence of 50° and an angle of refraction of 30°. Calculate the refractive index of the glass.
[3 marks]
Answer explanation
Draft walkthroughs are based on marking guidance, not independently verified derivations.
1. List the given quantities and the requested unknown. Choose the relation that connects them, state any required assumptions, then substitute before rounding. Preserve exact expressions when the task asks for an exact result.
2. Work through this mathematical step: Uses n = sin(angle of incidence)/sin(angle of refraction). Write the intermediate operation, keep the units consistent where applicable, and check the relation against the quantities given in the question.
3. Work through this mathematical step: Substitutes sin50°/sin30°. Write the intermediate operation, keep the units consistent where applicable, and check the relation against the quantities given in the question.
4. Develop this part of the answer: Obtains n ≈ 1.53. Show which detail or principle supports it and how it addresses the command; equivalent supported wording is acceptable.
5. Check the complete task again, including restrictions, units, precision and supporting evidence when relevant. Specific caution: Light bends towards the normal when entering a denser medium from a less dense one, so the angle of refraction is always smaller than the angle of incidence in this direction — consistent with n > 1 here.
Marking points
- Uses n = sin(angle of incidence)/sin(angle of refraction).
- Substitutes sin50°/sin30°.
- Obtains n ≈ 1.53.
Examiner tip: Light bends towards the normal when entering a denser medium from a less dense one, so the angle of refraction is always smaller than the angle of incidence in this direction — consistent with n > 1 here.
26.
Marking analysis: A learner attempts the following task: “A ray of light travels from air into a glass block, with an angle of incidence of 50° and an angle of refraction of 30°. Calculate the refractive index of the glass.” Their response addresses only this point: “Uses n = sin(angle of incidence)/sin(angle of refraction).” Evaluate the response against the complete 3-mark task. Identify what earns credit and state every additional requirement needed for full marks.
[3 marks]
Answer explanation
Draft walkthroughs are based on marking guidance, not independently verified derivations.
1. Separate the learner's stated response from the complete task. Credit only what their response demonstrates, then identify each missing requirement; do not assume unstated working.
2. Requirement 1: Recognises credit for the stated point: Uses n = sin(angle of incidence)/sin(angle of refraction). Compare this requirement with the supplied learner response; missing evidence cannot earn credit.
3. Requirement 2: Identifies the missing requirement: Substitutes sin50°/sin30°. Compare this requirement with the supplied learner response; missing evidence cannot earn credit.
4. Requirement 3: Identifies the missing requirement: Obtains n ≈ 1.53. Compare this requirement with the supplied learner response; missing evidence cannot earn credit.
5. Check the complete task again, including restrictions, units, precision and supporting evidence when relevant. Specific caution: Treat each marking point as a separate requirement. Do not award the same idea twice, and do not infer work the learner did not show.
Marking points
- Recognises credit for the stated point: Uses n = sin(angle of incidence)/sin(angle of refraction).
- Identifies the missing requirement: Substitutes sin50°/sin30°.
- Identifies the missing requirement: Obtains n ≈ 1.53.
Examiner tip: Treat each marking point as a separate requirement. Do not award the same idea twice, and do not infer work the learner did not show.
27.
The refractive index of a certain glass is 1.55. Calculate the critical angle for light travelling from this glass into air.
[3 marks]
Answer explanation
Draft walkthroughs are based on marking guidance, not independently verified derivations.
1. List the given quantities and the requested unknown. Choose the relation that connects them, state any required assumptions, then substitute before rounding. Preserve exact expressions when the task asks for an exact result.
2. Work through this mathematical step: Uses sin(critical angle) = 1/n. Write the intermediate operation, keep the units consistent where applicable, and check the relation against the quantities given in the question.
3. Work through this mathematical step: Substitutes 1/1.55. Write the intermediate operation, keep the units consistent where applicable, and check the relation against the quantities given in the question.
4. Develop this part of the answer: Obtains critical angle ≈ 40.2°. Show which detail or principle supports it and how it addresses the command; equivalent supported wording is acceptable.
5. Check the complete task again, including restrictions, units, precision and supporting evidence when relevant. Specific caution: The critical angle only applies to light travelling from a denser medium into a less dense one — beyond this angle, total internal reflection occurs instead of refraction.
Marking points
- Uses sin(critical angle) = 1/n.
- Substitutes 1/1.55.
- Obtains critical angle ≈ 40.2°.
Examiner tip: The critical angle only applies to light travelling from a denser medium into a less dense one — beyond this angle, total internal reflection occurs instead of refraction.
28.
Marking analysis: A learner attempts the following task: “The refractive index of a certain glass is 1.55. Calculate the critical angle for light travelling from this glass into air.” Their response addresses only this point: “Uses sin(critical angle) = 1/n.” Evaluate the response against the complete 3-mark task. Identify what earns credit and state every additional requirement needed for full marks.
[3 marks]
Answer explanation
Draft walkthroughs are based on marking guidance, not independently verified derivations.
1. Separate the learner's stated response from the complete task. Credit only what their response demonstrates, then identify each missing requirement; do not assume unstated working.
2. Requirement 1: Recognises credit for the stated point: Uses sin(critical angle) = 1/n. Compare this requirement with the supplied learner response; missing evidence cannot earn credit.
3. Requirement 2: Identifies the missing requirement: Substitutes 1/1.55. Compare this requirement with the supplied learner response; missing evidence cannot earn credit.
4. Requirement 3: Identifies the missing requirement: Obtains critical angle ≈ 40.2°. Compare this requirement with the supplied learner response; missing evidence cannot earn credit.
5. Check the complete task again, including restrictions, units, precision and supporting evidence when relevant. Specific caution: Treat each marking point as a separate requirement. Do not award the same idea twice, and do not infer work the learner did not show.
Marking points
- Recognises credit for the stated point: Uses sin(critical angle) = 1/n.
- Identifies the missing requirement: Substitutes 1/1.55.
- Identifies the missing requirement: Obtains critical angle ≈ 40.2°.
Examiner tip: Treat each marking point as a separate requirement. Do not award the same idea twice, and do not infer work the learner did not show.
29.
A car horn emits sound at a frequency of 500 Hz. The car moves towards a stationary observer at 30 m/s. Calculate the frequency heard by the observer, using f′ = fv/(v − vs), where v = 340 m/s is the speed of sound.
[4 marks]
Answer explanation
Draft walkthroughs are based on marking guidance, not independently verified derivations.
1. List the given quantities and the requested unknown. Choose the relation that connects them, state any required assumptions, then substitute before rounding. Preserve exact expressions when the task asks for an exact result.
2. Work through this mathematical step: States f′ = fv/(v − vs), for a source moving towards a stationary observer. Write the intermediate operation, keep the units consistent where applicable, and check the relation against the quantities given in the question.
3. Work through this mathematical step: Substitutes f′ = (500 × 340)/(340 − 30). Write the intermediate operation, keep the units consistent where applicable, and check the relation against the quantities given in the question.
4. Work through this mathematical step: Calculates the denominator: 340 − 30 = 310. Write the intermediate operation, keep the units consistent where applicable, and check the relation against the quantities given in the question.
5. Develop this part of the answer: Obtains f′ ≈ 548 Hz. Show which detail or principle supports it and how it addresses the command; equivalent supported wording is acceptable.
6. Check the complete task again, including restrictions, units, precision and supporting evidence when relevant. Specific caution: When the source moves towards the observer, vs is subtracted from v in the denominator, making the observed frequency higher than the emitted frequency — for a receding source, vs would instead be added.
Marking points
- States f′ = fv/(v − vs), for a source moving towards a stationary observer.
- Substitutes f′ = (500 × 340)/(340 − 30).
- Calculates the denominator: 340 − 30 = 310.
- Obtains f′ ≈ 548 Hz.
Examiner tip: When the source moves towards the observer, vs is subtracted from v in the denominator, making the observed frequency higher than the emitted frequency — for a receding source, vs would instead be added.
30.
Marking analysis: A learner attempts the following task: “A car horn emits sound at a frequency of 500 Hz. The car moves towards a stationary observer at 30 m/s. Calculate the frequency heard by the observer, using f′ = fv/(v − vs), where v = 340 m/s is the speed of sound.” Their response addresses only this point: “States f′ = fv/(v − vs), for a source moving towards a stationary observer.” Evaluate the response against the complete 4-mark task. Identify what earns credit and state every additional requirement needed for full marks.
[4 marks]
Answer explanation
Draft walkthroughs are based on marking guidance, not independently verified derivations.
1. Separate the learner's stated response from the complete task. Credit only what their response demonstrates, then identify each missing requirement; do not assume unstated working.
2. Requirement 1: Recognises credit for the stated point: States f′ = fv/(v − vs), for a source moving towards a stationary observer. Compare this requirement with the supplied learner response; missing evidence cannot earn credit.
3. Requirement 2: Identifies the missing requirement: Substitutes f′ = (500 × 340)/(340 − 30). Compare this requirement with the supplied learner response; missing evidence cannot earn credit.
4. Requirement 3: Identifies the missing requirement: Calculates the denominator: 340 − 30 = 310. Compare this requirement with the supplied learner response; missing evidence cannot earn credit.
5. Requirement 4: Identifies the missing requirement: Obtains f′ ≈ 548 Hz. Compare this requirement with the supplied learner response; missing evidence cannot earn credit.
6. Check the complete task again, including restrictions, units, precision and supporting evidence when relevant. Specific caution: Treat each marking point as a separate requirement. Do not award the same idea twice, and do not infer work the learner did not show.
Marking points
- Recognises credit for the stated point: States f′ = fv/(v − vs), for a source moving towards a stationary observer.
- Identifies the missing requirement: Substitutes f′ = (500 × 340)/(340 − 30).
- Identifies the missing requirement: Calculates the denominator: 340 − 30 = 310.
- Identifies the missing requirement: Obtains f′ ≈ 548 Hz.
Examiner tip: Treat each marking point as a separate requirement. Do not award the same idea twice, and do not infer work the learner did not show.
31.
An autonomous survey boat sends a short sound pulse vertically downward in freshwater. The echo returns 0.0720 s later. The speed of sound in the water is 1480 m s⁻¹ and the timing uncertainty is ±0.0010 s. (a) Calculate the water depth. (b) Determine the percentage uncertainty in the depth due to timing. (c) Explain why an echo is produced at the lake bed.
[4 marks]
Answer explanation
Draft walkthroughs are based on marking guidance, not independently verified derivations.
1. List the given quantities and the requested unknown. Choose the relation that connects them, state any required assumptions, then substitute before rounding. Preserve exact expressions when the task asks for an exact result.
2. Work through this mathematical step: Recognises the pulse travels twice the depth and uses d = vt/2. Write the intermediate operation, keep the units consistent where applicable, and check the relation against the quantities given in the question.
3. Work through this mathematical step: Obtains d = 1480(0.0720)/2 = 53.3 m. Write the intermediate operation, keep the units consistent where applicable, and check the relation against the quantities given in the question.
4. Work through this mathematical step: Calculates percentage uncertainty = (0.0010/0.0720) × 100 ≈ 1.4%. Write the intermediate operation, keep the units consistent where applicable, and check the relation against the quantities given in the question.
5. Develop this part of the answer: Explains that part of the wave is reflected because the water and lake bed have different acoustic impedances/properties. Show which detail or principle supports it and how it addresses the command; equivalent supported wording is acceptable.
6. Check the complete task again, including restrictions, units, precision and supporting evidence when relevant. Specific caution: Echo time is a round-trip time. Dividing by two is part of the model, not an uncertainty adjustment.
Marking points
- Recognises the pulse travels twice the depth and uses d = vt/2.
- Obtains d = 1480(0.0720)/2 = 53.3 m.
- Calculates percentage uncertainty = (0.0010/0.0720) × 100 ≈ 1.4%.
- Explains that part of the wave is reflected because the water and lake bed have different acoustic impedances/properties.
Examiner tip: Echo time is a round-trip time. Dividing by two is part of the model, not an uncertainty adjustment.
32.
Marking analysis: A learner attempts the following task: “An autonomous survey boat sends a short sound pulse vertically downward in freshwater. The echo returns 0.0720 s later. The speed of sound in the water is 1480 m s⁻¹ and the timing uncertainty is ±0.0010 s. (a) Calculate the water depth. (b) Determine the percentage uncertainty in the depth due to timing. (c) Explain why an echo is produced at the lake bed.” Their response addresses only this point: “Recognises the pulse travels twice the depth and uses d = vt/2.” Evaluate the response against the complete 4-mark task. Identify what earns credit and state every additional requirement needed for full marks.
[4 marks]
Answer explanation
Draft walkthroughs are based on marking guidance, not independently verified derivations.
1. Separate the learner's stated response from the complete task. Credit only what their response demonstrates, then identify each missing requirement; do not assume unstated working.
2. Requirement 1: Recognises credit for the stated point: Recognises the pulse travels twice the depth and uses d = vt/2. Compare this requirement with the supplied learner response; missing evidence cannot earn credit.
3. Requirement 2: Identifies the missing requirement: Obtains d = 1480(0.0720)/2 = 53.3 m. Compare this requirement with the supplied learner response; missing evidence cannot earn credit.
4. Requirement 3: Identifies the missing requirement: Calculates percentage uncertainty = (0.0010/0.0720) × 100 ≈ 1.4%. Compare this requirement with the supplied learner response; missing evidence cannot earn credit.
5. Requirement 4: Identifies the missing requirement: Explains that part of the wave is reflected because the water and lake bed have different acoustic impedances/properties. Compare this requirement with the supplied learner response; missing evidence cannot earn credit.
6. Check the complete task again, including restrictions, units, precision and supporting evidence when relevant. Specific caution: Treat each marking point as a separate requirement. Do not award the same idea twice, and do not infer work the learner did not show.
Marking points
- Recognises credit for the stated point: Recognises the pulse travels twice the depth and uses d = vt/2.
- Identifies the missing requirement: Obtains d = 1480(0.0720)/2 = 53.3 m.
- Identifies the missing requirement: Calculates percentage uncertainty = (0.0010/0.0720) × 100 ≈ 1.4%.
- Identifies the missing requirement: Explains that part of the wave is reflected because the water and lake bed have different acoustic impedances/properties.
Examiner tip: Treat each marking point as a separate requirement. Do not award the same idea twice, and do not infer work the learner did not show.