Cambridge International AS & A Level · 7 · structured
Read a wave and derive its speed relationship
Read a wave and derive its speed relationship · Original GioPhysics question with a detailed, mark-by-mark answer guide.
- Demand
- demanding
- Marks
- 17
- Topics
- 4
- Answer
- Complete
A sinusoidal transverse wave travels right. A displacement–distance snapshot has successive zero/upward-crossing at x=0, crest+3.0 mm at 0.20m, zero at 0.40m, trough−3.0 mm at 0.60m, and next zero/upward-crossing at 0.80m. At the fixed equilibrium position x=0, the time trace is 0 at t0,−3.0 mm at 0.010s,0 at 0.020s,+3.0 mm at 0.030s, and0 at 0.040s before repeating.
- (a)
Define displacement, amplitude, wavelength, period, frequency, wave speed and phase difference. Read amplitude, wavelength and period from the data, calculate frequency, and find the phase-difference magnitude between positions0.10m and0.30m.
9 marks - (b)
Derive v=fλ from definitions rather than quoting it, then find the speed of this wave.
4 marks - (c)
Contrast this material wave with electromagnetic waves in free space: state the electromagnetic oscillation direction relative to travel and whether radio and gamma waves have different vacuum speeds.
2 marks - (d)
A marked section of the rope returns to its original position after one period, yet a pulse can lift a small hanging tag farther along the rope. Explain what a progressive wave transfers and why that does not require bulk transport of rope material.
2 marks
Ready to self-mark?Reveal the detailed answer guide
(a)
Define displacement, amplitude, wavelength, period, frequency, wave speed and phase difference. Read amplitude, wavelength and period from the data, calculate frequency, and find the phase-difference magnitude between positions0.10m and0.30m.
Identify what the question is testing, organise the response into distinct mark-earning points, and make every conclusion traceable to a physical principle or to the evidence supplied.
- 1
Give all seven definitions with spatial/time distinction.
- 2
Identify3.0 mm peak magnitude,0.80m equivalent-position separation and0.040s repeat time.
- 3
Invert period for25 Hz.
- 4
Convert quarter-wavelength separation to 90° orπ/2rad.
- 5
Allocation: displacement/amplitude definitions (1); wavelength/wave-speed definitions (1); period/frequency definitions (1); phase-difference definition (1); amplitude reading (1); wavelength reading (1); period reading (1); frequency calculation (1); phase calculation (1).
(b)
Derive v=fλ from definitions rather than quoting it, then find the speed of this wave.
List the given quantities with units, identify the required quantity, write the governing relationship before substituting, and keep extra digits until the final line so rounding does not distort the result.
- 1
Identify distanceλ travelled by the pattern during oneT.
- 2
Apply speed=distance/time.
- 3
Use frequency=1/T.
- 4
Calculate20m s⁻¹.
(c)
Contrast this material wave with electromagnetic waves in free space: state the electromagnetic oscillation direction relative to travel and whether radio and gamma waves have different vacuum speeds.
Identify what the question is testing, organise the response into distinct mark-earning points, and make every conclusion traceable to a physical principle or to the evidence supplied.
- 1
State transverse electromagnetic fields relative to propagation.
- 2
State common c in free space, independent of band.
(d)
A marked section of the rope returns to its original position after one period, yet a pulse can lift a small hanging tag farther along the rope. Explain what a progressive wave transfers and why that does not require bulk transport of rope material.
Identify what the question is testing, organise the response into distinct mark-earning points, and make every conclusion traceable to a physical principle or to the evidence supplied.
- 1
Identify energy transferred to the distant tag.
- 2
Distinguish this from bulk movement of rope material, which oscillates locally.
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.
- (a) Give all seven definitions with spatial/time distinction.
- (a) Identify3.0 mm peak magnitude,0.80m equivalent-position separation and0.040s repeat time.
- (a) Invert period for25 Hz.
- (a) Convert quarter-wavelength separation to 90° orπ/2rad.
- (a) Allocation: displacement/amplitude definitions (1); wavelength/wave-speed definitions (1); period/frequency definitions (1); phase-difference definition (1); amplitude reading (1); wavelength reading (1); period reading (1); frequency calculation (1); phase calculation (1).
- (b) Identify distanceλ travelled by the pattern during oneT.
- (b) Apply speed=distance/time.
- (b) Use frequency=1/T.
- (b) Calculate20m s⁻¹.
- (c) State transverse electromagnetic fields relative to propagation.
- (c) State common c in free space, independent of band.
- (d) Identify energy transferred to the distant tag.
- (d) Distinguish this from bulk movement of rope material, which oscillates locally.
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