The distance between two successive trough points of a wave is

Analysis

The question asks for the definition of the distance between two consecutive points in the same phase on a transverse wave, specifically two successive troughs.

Concept Explanation

In wave motion, a wavelength ($\lambda$) is defined as the distance between two successive points that are in phase.

• A trough is the lowest point of a wave cycle.
• A crest is the highest point of a wave cycle.

Because a wave repeats its pattern periodically, the distance from one crest to the next consecutive crest is one full wavelength. Similarly, the distance from one trough to the next consecutive trough is also exactly one full wavelength.

Step-by-Step Solution

1. Visualize the wave: Imagine a sine wave moving along a horizontal axis.
2. Identify the points: Mark the lowest point (trough) of the first cycle and the lowest point (trough) of the immediate next cycle.
3. Measure the distance: The horizontal distance covered by one complete cycle (from crest to crest or trough to trough) represents one full oscillation.
4. Apply the definition: By definition, the distance between two successive points in phase (like two consecutive troughs) is equal to one wavelength ($\lambda$).

Conclusion

The distance between two successive troughs is equal to one wavelength. This matches option B.

Exam Tip

Always remember the "In-Phase" rule: Any two consecutive points that are at the same position and moving in the same direction on a wave are exactly one wavelength apart. This applies to crest-to-crest, trough-to-trough, or even any two points on the equilibrium line that are moving in the same direction.