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Advanced Physics Recap – Wave Propagation | Ronnie (2026)

Wave Propagation

Ronnie (2026)

Tuesday, 25 August 2026

01

Nature of Waves · Foundation

Energy transfer without net matter transfer

A cork is floating on still water. A train of water waves travels from left to right and passes the cork. After the complete wave train has passed, the cork is found close to its original horizontal position.

Wave direction Cork Local oscillation

The cork oscillates locally while the wave disturbance propagates across the water surface.

  1. Explain why the cork does not travel continuously to the right with the wave.
  2. State what is transferred from left to right by the wave.
  3. Distinguish between the motion of the wave and the motion of the cork.
4 marks
02

Oscillation · Period and Frequency

Reading a displacement–time graph

The graph shows the displacement of one particle in a medium as it oscillates. The graph describes the motion of one particle; it does not show the physical shape of the complete wave.

0 0.2 0.4 0.6 0.8 1.0 1.2 1.4 1.6 +4 0 −4 Time / s Displacement / cm

Displacement–time graph for a single oscillating particle.

  1. Determine the amplitude of the oscillation.
  2. Determine the period and frequency.
  3. State the particle’s direction of motion at t = 0.4 s.
  4. At which labelled times between 0 and 1.6 s is the particle momentarily at rest?
  5. Explain why the particle’s speed is greatest when its displacement is zero.
7 marks
03

Wave Classification

Transverse and longitudinal waves

The diagrams represent two different types of travelling waves. The red arrows show the direction in which particles of the medium oscillate. The blue arrows show the direction of propagation of the wave.

Wave A Wave B Wave propagation Particle motion is perpendicular Wave propagation Particle motion is parallel Compression Rarefaction

Wave A shows perpendicular particle motion. Wave B shows compressions and rarefactions.

  1. Identify Wave A and Wave B as transverse or longitudinal.
  2. Explain your classification using the particle motion and wave direction.
  3. State whether a sound wave travelling through air is represented by A or B.
  4. State whether an electromagnetic wave is represented by A or B.
  5. Explain why sound cannot travel through a vacuum, while an electromagnetic wave can.
7 marks
04

Travelling Wave Direction

Using particle motion to determine wave direction

The graph shows the shape of a transverse wave on a string at one instant. Particle P is moving vertically upward at the instant shown.

A P Q R S P moves upward Equilibrium position

P lies on a section of the wave with a negative spatial slope.

  1. Deduce whether the wave is travelling to the left or to the right. Explain your reasoning.
  2. State the instantaneous direction of motion of Q and S.
  3. Identify the labelled particles that are momentarily at rest.
  4. Identify the labelled particles with maximum particle speed.
  5. State the acceleration direction of A and R.
8 marks
05

Wave Snapshots · Quantitative Reasoning

Comparing two displacement–distance graphs

The diagrams show the same sinusoidal travelling wave at t = 0 and t = 0.15 s. Each horizontal grid interval represents 2.0 m. The wave moves by less than one complete wavelength during the 0.15 s interval.

t = 0 t = 0.15 s Apparent shift = 2.0 m 2.0 m

Corresponding crests have shifted one horizontal grid interval to the right.

  1. Determine the wavelength of the wave.
  2. Determine the direction of propagation.
  3. Calculate the wave speed.
  4. Calculate the period and frequency.
  5. Explain why, without the statement that the wave moved by less than one wavelength, the two snapshots would not give a unique wave speed.
9 marks
06

Particle Dynamics and Energy

Speed, acceleration, kinetic energy and potential energy

The diagram shows one complete wavelength of a sinusoidal transverse wave travelling to the right. All labelled particles belong to the same uniform string and oscillate with the same amplitude and frequency.

Wave travels right A B C D E F +A −A

A and E are at extreme displacements. C and F are at equilibrium.

  1. Which particles are momentarily at rest?
  2. Which particles have maximum speed and maximum kinetic energy?
  3. Which particles have maximum acceleration magnitude?
  4. Compare the speed magnitudes of B and D.
  5. Compare the potential energies of B and D.
  6. State the direction of motion of B, C, D and F.
  7. A student claims that particle A has a larger amplitude than particle C because A is currently farther from equilibrium. Explain why this is incorrect.
11 marks
07

Finite Wave Train · Synthesis

Arrival time, duration and particle oscillation

A vibrator at the left end of a long uniform string oscillates sinusoidally for exactly three complete cycles and then stops at its equilibrium position. The vibrator frequency is 4.0 Hz and the wave speed is 6.0 m s−1. Particle P is located 12 m from the vibrator.

Source Direction of propagation P 12 m

The diagram is schematic. Particle P remains at a fixed horizontal position and oscillates only when the wave train reaches it.

  1. Calculate the period of the vibrator.
  2. Calculate the wavelength of the wave.
  3. Determine how long the vibrator operates.
  4. Determine the physical length of the complete three-cycle wave train.
  5. At what time after the vibrator starts does P first begin to oscillate?
  6. At what time does P stop oscillating?
  7. How many complete oscillations does P perform?
  8. After the wave train has passed, is P permanently displaced from its original equilibrium position?
  9. Explain whether any individual string particle has travelled the full 12 m from the vibrator to P.
13 marks

Question 1

  1. The cork is a particle or object within the medium. It oscillates around its own equilibrium position rather than travelling continuously with the wave.
  2. Energy and the wave disturbance are transferred from left to right.
  3. The wave pattern propagates horizontally across the surface. The cork undergoes local oscillatory motion, mainly upward and downward, with no large net horizontal displacement after the complete wave train passes.
A wave transfers energy without producing a net transfer of matter over a large distance.

Question 2

  1. The maximum displacement from equilibrium is 4.0 cm.
  2. Consecutive crests occur at 0.2 s and 1.0 s. Therefore:
T = 1.0 − 0.2 = 0.80 s
f = 1/T = 1/0.80 = 1.25 Hz
  1. At 0.4 s, the displacement is zero and the graph has a negative gradient. The particle is therefore moving in the negative displacement direction.
  2. The particle is momentarily at rest at the positive and negative extreme displacements: 0.2 s, 0.6 s, 1.0 s and 1.4 s.
  3. At equilibrium, the restoring potential energy is minimum and the kinetic energy is maximum. Therefore, the particle has its maximum speed while crossing zero displacement.

Question 3

  1. Wave A is transverse. Wave B is longitudinal.
  2. In Wave A, particle oscillation is perpendicular to the direction of propagation. In Wave B, particle oscillation is parallel to the direction of propagation.
  3. A sound wave travelling through air is represented by Wave B. It consists of compressions and rarefactions.
  4. An electromagnetic wave is represented by Wave A because it is transverse.
  5. Sound is a mechanical wave. It requires particles of a material medium to oscillate and transfer energy. A vacuum contains no particles, so sound cannot propagate through it.
An electromagnetic wave does not require a material medium. It transfers energy through oscillating electric and magnetic fields and can therefore travel through a vacuum.

Question 4

  1. P lies on a section with a negative spatial slope. P is moving upward. For this to occur, the waveform must be shifting toward the right.
  2. Q lies on the same descending section as P, so Q is moving upward. S lies on an ascending section, so S is moving downward.
  3. A and R are at extreme displacements. They are therefore momentarily at rest.
  4. Q and S are at equilibrium, so they have maximum particle speed.
  5. A is above equilibrium, so it accelerates downward. R is below equilibrium, so it accelerates upward. Both accelerations point toward equilibrium.
For a right-moving transverse wave:
particle velocity has the opposite sign to the local spatial slope.

Question 5

  1. The distance between consecutive crests is four horizontal intervals.
λ = 4 × 2.0 m = 8.0 m
  1. Corresponding crests have shifted one interval to the right. Therefore, the wave travels to the right.
  2. The wave moves 2.0 m in 0.15 s.
v = distance/time
v = 2.0/0.15
v = 13.3 m s−1
  1. Using v = fλ:
f = v/λ = 13.3/8.0 = 1.67 Hz
T = 1/f = 0.60 s
  1. A periodic waveform looks identical after moving through any whole number of complete wavelengths. Without the stated restriction, the wave could have travelled:
distance = 2.0 m + n(8.0 m)
where n = 0, 1, 2, 3, …

Therefore, the two snapshots alone would allow several possible speeds. The condition that the wave moved by less than one wavelength selects the minimum shift of 2.0 m.

Question 6

  1. A and E are at maximum positive and maximum negative displacement. They are momentarily at rest.
  2. C and F are crossing equilibrium. They have maximum particle speed and maximum kinetic energy.
  3. A and E have maximum acceleration magnitude because their displacement magnitudes are maximum.
  4. B and D are equally far from equilibrium. Their speed magnitudes are therefore equal.
  5. Potential energy depends on the magnitude of displacement from equilibrium. Since B and D have equal displacement magnitudes, their potential energies are equal.
  6. The wave travels right, so particle velocity is opposite in sign to the local slope:
    • B moves upward.
    • C moves upward.
    • D moves upward.
    • F moves downward.
  7. Amplitude is the maximum displacement that a particle can attain during its oscillation. It is not the particle’s displacement at one particular instant.
Since all particles on this ideal uniform wave oscillate with the same amplitude, particle A and particle C have the same amplitude. A is currently at its amplitude, while C is currently passing through equilibrium.

Question 7

  1. The period is:
T = 1/f = 1/4.0 = 0.25 s
  1. The wavelength is:
λ = v/f = 6.0/4.0 = 1.5 m
  1. The source completes three periods:
Source operating time = 3T
= 3 × 0.25
= 0.75 s
  1. The wave train contains three complete wavelengths:
Length = 3λ
= 3 × 1.5
= 4.5 m
  1. The front of the wave train must travel 12 m before P begins to oscillate:
Arrival time = distance/speed
= 12/6.0
= 2.0 s
  1. P oscillates for the same duration as the source, which is 0.75 s.
Stopping time = 2.0 + 0.75
= 2.75 s
  1. P performs three complete oscillations.
  2. P is not permanently displaced. Since the source completes three full cycles and stops at equilibrium, P returns to its original equilibrium position after the complete wave train has passed.
  3. No individual string particle travels the full 12 m. Each particle oscillates transversely around its own fixed equilibrium position.
The disturbance and energy travel 12 m along the string. Matter does not undergo a net transfer from the source to particle P.
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