Standing waves are produced by

Analysis of the Question

The question asks for the physical condition required to produce standing waves (also known as stationary waves). We need to distinguish these from progressive (traveling) waves.

Concept Explanation

A standing wave is formed when two waves of the same frequency and amplitude travel in opposite directions through the same medium and interfere with each other.

In a practical setting, this usually happens when a wave travels toward a boundary (like a fixed end of a string or a closed pipe), reflects off that boundary, and travels back in the opposite direction. As the incident wave and the reflected wave overlap, they create a pattern where certain points (nodes) appear to be stationary, while others (antinodes) vibrate with maximum amplitude.

Step-by-Step Solution

1. Identify the mechanism: Standing waves are not caused by the Doppler effect (which relates to the motion of a source toward or away from an observer, as mentioned in options B and C).
2. Analyze the interference: For a standing wave to exist, the wave must be "trapped." This happens when a wave hits a boundary and reflects.
3. Superposition: The reflected wave travels back and meets the incoming wave. Because they have the same frequency and speed but are moving in opposite directions, they undergo superposition (interference).
4. Result: This interference creates a stationary pattern in the medium. This confirms that reflection and interference are the essential requirements.

Evaluation of Options

• A: Incorrect. Standing waves are named for the stationary nodes, not because they vibrate in a vertical plane.
• B & C: Incorrect. These describe the Doppler Effect, which causes a shift in observed frequency, not the formation of standing waves.
• D: Correct. This accurately describes the process of reflection and superposition necessary to create a standing wave.

Exam Tip

Whenever you see "Standing Wave" or "Stationary Wave" in a JAMB or WASSCE question, look for keywords like "reflection," "superposition," "opposite directions," or "nodes and antinodes." If the question mentions "source moving," it is almost certainly referring to the Doppler Effect, not standing waves!