Wave models, quantities, graphs and transfer
Key idea: H2 Physics lessons on progressive-wave models, standing waves, interference, diffraction and resolution.
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The core idea
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Big question: How do displacement graphs represent a travelling wave?
A displacement–distance graph is a snapshot across space; a displacement–time graph follows one point. Both show amplitude, but wavelength belongs to the spatial graph and period to the time graph. Progressive waves transfer energy without net transfer of matter, obey v = fλ, and may be longitudinal or transverse depending on the oscillation direction.
Follow the oscillation and the pattern separately
A progressive wave transfers energy from place to place while particles of a material medium oscillate about equilibrium. The particles do not travel with the wave. Electromagnetic waves need no material medium: their electric and magnetic fields oscillate as energy travels.
A displacement–time graph follows one fixed position, so one horizontal cycle is the period T. A displacement–distance graph is a snapshot at one instant, so one horizontal cycle is the wavelength λ. Their shapes can look identical, but their axes and meanings are different.
Check your understanding: On which graph can a horizontal separation give phase difference using 2πΔx/λ?
A displacement–distance graph at one instant. On a time graph use 2πΔt/T.
Connect speed, phase and wave type
One wavelength passes a point in one period, giving v = λ/T = fλ. Phase difference records the fraction of a cycle separating two oscillations: Δφ = 2πΔx/λ at one time or 2πΔt/T at one position.
In a transverse wave the oscillation is perpendicular to travel; in a longitudinal wave it is parallel. A longitudinal displacement graph plots signed particle displacement, not pressure. Compressions occur where displacement changes most steeply, not automatically at displacement peaks.
Check your understanding: Two points are separated by 0.75λ. What is their smallest phase difference?
1.5π rad, equivalent to −π/2 rad depending on which point leads.
Key ideas to keep
- Do not read wavelength from a time graph or period from a distance graph.
- Wave speed is not the same as particle oscillation speed.
- Phase difference follows the corresponding fraction of a cycle.
See the reasoning
Worked example
Read speed and phase from two representations
Question: A spatial profile gives λ = 0.80 m. At one position, successive crests pass 0.25 s apart. Find wave speed and the phase difference between points 0.30 m apart.
Step 1: Read the correct cycles
Why: Wavelength comes from space; period comes from time.
Working: λ = 0.80 m and T = 0.25 s, so f = 1/T = 4.0 Hz.
Step 2: Find propagation speed
Why: One wavelength advances per period.
Working: v = fλ = 4.0(0.80) = 3.2 m s⁻¹.
Step 3: Convert separation to phase
Why: The two points are compared at one instant.
Working: Δφ = 2πΔx/λ = 2π(0.30/0.80) = 0.75π rad.
Answer: The speed is 3.2 m s⁻¹ and the phase difference is 0.75π rad.
Check: The phase is below π because the separation is below half a wavelength.
Another worked model
Question
Two points 0.15 m apart on a 0.60 m wavelength are compared at one instant. Find their phase difference. If frequency is 12 Hz, derive and find wave speed.
Check the worked solution
Δφ = 2πΔx/λ = 2π(0.15/0.60) = π/2 rad. In one period T, a crest advances one wavelength λ, so v = λ/T = fλ = 12(0.60) = 7.2 m s⁻¹.
Use a hint if needed
Practise with support
Try this
A longitudinal wave has compression spacing 0.45 m and frequency 800 Hz. Find speed and the phase difference between points 0.15 m apart, then state how to sketch its spatial graph.
Hint: Successive compressions are one wavelength apart; phase uses 2πΔx/λ.
Check your answer
v = fλ = 800(0.45) = 360 m s⁻¹. Δφ = 2π(0.15/0.45) = 2π/3 rad. A displacement graph still plots signed particle displacement against position; compressions are represented through particle crowding or pressure, not by calling the wave transverse.
Now work without the hint
Practise independently
Your turn
A wave travels 18 m in 0.060 s and has wavelength 0.75 m. Find speed, frequency and period. Explain why the medium has no net displacement after many cycles.
Check your answer
v = 18/0.060 = 300 m s⁻¹, f = v/λ = 400 Hz and T = 1/f = 2.50 ms. Medium particles oscillate about fixed equilibrium positions, so their cycle-average displacement is zero even though the wave transfers energy.
Avoid these traps
Common mistakes
Common mistake
A progressive wave carries particles from source to receiver.
What is wrong with this reasoning?
Show better thinking
Particles of a mechanical medium oscillate about equilibrium; the disturbance and energy progress without net matter transfer.
Common mistake
Horizontal crest spacing always represents wavelength.
What is wrong with this reasoning?
Show better thinking
It is wavelength only on a displacement–position graph at one instant. On a displacement–time graph at one position, crest spacing is period.
Write for the examiner
Exam guidance
Label which variable is held fixed before reading a wave graph.
Exam-style practice [7 marks]
A student is given an unlabelled sinusoidal graph and says its peak spacing is the wavelength. Explain what must be known before that conclusion is valid, then describe how to use suitable time and distance information to find wave speed and phase difference.
Plan before you answer
- Identify what is fixed and read the axis units.
- Define period and wavelength from their proper graphs.
- Use v = fλ and the matching phase relation.
Mark your answer and compare the model
Marking points
Tick each point only if your answer states it clearly.
Model answer
Peak spacing is a wavelength only if the horizontal axis is distance and the graph is a snapshot at one instant. If it is time at one position, peak spacing is a period. Read λ from the spatial graph and T from the time graph, calculate f = 1/T and then v = fλ. Compare points at one instant with Δφ = 2πΔx/λ, or events at one point with Δφ = 2πΔt/T.
Come back in three days
Check what stayed with you
Recall question 1
What travels in a progressive mechanical wave?
Check the answer
Energy and the wave pattern; medium particles only oscillate about equilibrium.
Recall question 2
What does one horizontal cycle mean on a displacement–time graph?
Check the answer
One period.
Recall question 3
State the wave equation.
Check the answer
v = fλ.
Syllabus and review details
This lesson covers the listed H2 Physics 9478 outcomes. Topic 10 states no explicit exclusions. Topic 11(j) does not require knowledge of spectrometer structure or use. Graph interpretations distinguish time traces at one position from spatial profiles at one instant, and all small-angle equations are used only with their stated geometry.
- GCE A-Level H2 PhysicsTopic 10(a) / Topic 10(b) / Topic 10(c) / Topic 10(d) / Topic 10(e) / Topic 10(f) · 2027Checked against the syllabus · partial topic coverageOfficial 9478 syllabus
Course and syllabus information
- Course
- GCE A-Level H2 Physics
- Edition
- GCE A-Level H2 Physics 2027