AQA AS Level Physics Paper 2, June 2025: Question 15

Circular Water Wave Reflection in a Cylindrical Beaker

AQA AS Level Physics • Section A / Multiple Choice • Waves

What this question tests

This question evaluates your ability to apply the wave kinematics equation ( distance = speed × time ) to circular wave propagation, recognize physical boundary constraints (beaker radius vs diameter), and deduce the behavior of a wave upon reflection at a fixed circular boundary.

Question 15 (1 Mark)

Multiple Choice Analysis & Step-by-Step Solution

✅ Correct Option: A

Radius of wave = 50 mm and Direction of travel = towards centre.

📐 Step-by-Step Calculation

Find the beaker radius:
The diameter is 200 mm , so the distance from the centre to the beaker wall is:
R = 200 mm / 2 = 100 mm
Calculate total distance travelled in 1.0 s:
d = v × t = 150 mm s⁻¹ × 1.0 s = 150 mm
Analyse boundary reflection:
The wave travels outwards from the centre and hits the wall after travelling 100 mm (at t = 0.67 s ).
Determine position and direction after reflection:
Remaining distance to travel:
150 mm − 100 mm = 50 mm
Because it reflects off the wall, it now travels inwards towards the centre.
Calculate radius of the wave ring:
Distance from centre = 100 mm − 50 mm = 50 mm .

💡 Key Physics Concepts

Wave Generation: Dipping a point source (pencil) into water creates circular wavefronts that propagate radially outwards.
Boundary Reflection: When water ripples encounter a rigid barrier (the beaker wall), they reflect back into the medium. For a circular boundary, an expanding circle reflects as a contracting circle focusing back toward the centre.
Radius vs. Diameter: The source is at the centre. Thus, the maximum possible outward distance before reflection is the radius ( 100 mm ), not the diameter ( 200 mm ).

Examiner Visualization Note:
If sketching this: Draw a circle representing the beaker with radius 100 mm . Mark the centre. Draw a dotted concentric circle at r = 50 mm with arrows pointing inward towards the centre to represent the reflected wavefront at t = 1.0 s .

❌ Common Traps & Errors

Selecting C or D (Radius = 150 mm): Students simply calculate 150 × 1.0 = 150 mm and forget the beaker only has a radius of 100 mm . A wave cannot travel 150 mm outward without hitting the wall!
Diameter Confusion: Assuming the wall is 200 mm away from the centre. This leads to thinking the wave has not yet reached the edge at 150 mm , incorrectly choosing D.
Incorrect Direction (Option B): Calculating 50 mm correctly by subtraction, but failing to realise that after bouncing off the outer boundary, the wave must travel towards the centre.

🧠 Exam Technique: Two-Column Elimination

This is a classic 2-variable multiple-choice question:

Direction First: Since d = 150 mm is greater than the container's radius ( 100 mm ), the wave must have already bounced off the wall. Therefore, it has reversed direction and must be heading towards centre. This immediately eliminates B and D!
Sanity Check on Radius: The container only extends to r = 100 mm . A circular wave inside this beaker can never have a radius of 150 mm . This rules out C and confirms A in seconds.