In wave terminology, the wavelength of a periodic wave is defined as the distance between which two points on the wave?

Introduction / Context:
Understanding the basic terms used to describe waves is essential in physics. One of the most important quantities is the wavelength, which is directly related to the wave's energy and frequency. This question asks you to identify which points along a wave can be used to measure one full wavelength.

Given Data / Assumptions:

• We are dealing with a periodic wave, such as a sinusoidal transverse wave drawn as a graph of displacement versus position.
• Crests are the highest points of the wave, and troughs are the lowest points.
• We must specify what distance corresponds to one complete cycle of the wave.
• We assume the wave repeats regularly, so the pattern of crests and troughs is periodic.

Concept / Approach:
The wavelength is defined as the distance between any two successive points on a wave that are in the same phase, meaning they have the same displacement and move in the same direction at the same time. In a standard waveform, the easiest such pairs are two successive crests or two successive troughs. The distance from any crest to the next crest, or from any trough to the next trough, is exactly one wavelength. The distance from a crest to a trough is only half a wavelength, because it covers half of the full oscillation.

Step-by-Step Solution:
Step 1: Recall the formal definition of wavelength: the spatial period of the wave, or the distance over which the wave's shape repeats. Step 2: On a graph, pick one crest, which is the highest point. The very next crest in the same pattern marks one full cycle later. Step 3: The distance between these two successive crests is one complete wavelength. Step 4: Similarly, the distance between one trough (the lowest point) and the next trough is also one full wavelength. Step 5: The distance between a crest and the nearest trough is only half a cycle, that is, half a wavelength, so it does not match the definition.

Verification / Alternative check:
If you mark a point anywhere on the wave, say where the displacement is zero and the motion is going upward, and then measure to the next identical point in the pattern (same displacement and direction of motion), that distance will be one wavelength. For sinusoidal waves, the crest to crest and trough to trough distances especially highlight this repetition. A crest to trough distance is shorter and clearly represents only part of the full oscillation, confirming that it cannot define the full wavelength by itself.

Why Other Options Are Wrong:
Crest and trough: The distance between a crest and the nearest trough corresponds to half a wavelength, not the full wavelength.

Crest and crest: Correct, because successive crests are one full cycle apart.
Trough and trough: Also correct, because successive troughs are one full cycle apart.

Common Pitfalls:
A very common mistake is to assume that the “height” of the wave, from crest to trough, defines the wavelength. In fact, that vertical distance corresponds to twice the amplitude, not the wavelength. Wavelength is always measured along the direction of propagation (horizontally on a standard graph), between points that are in the same phase. Remembering that “like to like” points such as crest to crest or trough to trough give the wavelength helps avoid confusion.

Final Answer:
The wavelength of a wave is the distance between Both B & C, that is, between successive crests or between successive troughs.