In wave physics, what is the correct way to measure the wavelength of a periodic wave when it is shown on a graph or oscilloscope screen?

Introduction / Context:
Wavelength is one of the most important quantities used to describe periodic waves in physics, including sound waves, water waves, and electromagnetic waves. It tells us the spatial length of one complete cycle of the wave pattern. When waves are drawn on a graph of displacement versus distance or on an oscilloscope screen, we can see repeating peaks and troughs. This question checks whether you know the standard textbook definition of wavelength and how to identify it correctly on such a graph.

Given Data / Assumptions:
• The wave is periodic, so its shape repeats regularly in space. • The graph shows clear peaks, also called crests, and troughs, which are the lowest points. • We are asked about the correct distance that represents one wavelength. • We assume the graph is plotted as displacement versus position along the wave.

Concept / Approach:
The standard definition of wavelength in physics is the distance between two neighbouring points that are in exactly the same phase of the wave. Points in the same phase have the same displacement and are moving in the same direction at the same time. For a simple sinusoidal wave, this means from crest to crest, from trough to trough, or between any two equivalent phase points separated by one full cycle. However, from crest to nearest trough is only half of a full cycle, because the wave has gone from maximum positive displacement to maximum negative displacement. Therefore, the distance from crest to crest (or trough to trough) is the correct measure of one full wavelength.

Step-by-Step Solution:
Step 1: Recall that wavelength is defined as the distance over which the wave pattern repeats itself. Step 2: Identify two neighbouring points on the graph that are in the same phase of the oscillation. Step 3: Notice that a crest is a convenient phase reference point because it is the highest point of the wave. Step 4: Measure the distance from one crest to the next crest along the horizontal axis, which represents position. Step 5: Recognise that this distance includes one entire rise and fall of the wave, that is, one full cycle. Step 6: Conclude that the distance from crest to crest is the correct way to measure one wavelength.

Verification / Alternative check:
As an alternative view, you can check with a trough instead of a crest. If you measure from one trough to the next trough, you will get the same distance as from crest to crest, which confirms that the wave repeats over that length. You can also see that going from crest to trough or trough to crest represents only half of the repeating pattern, because the wave still needs to return to the starting phase. In mathematical descriptions of sinusoidal waves, the spatial period is defined so that points separated by this distance differ in phase by 2 pi radians, not pi radians, which again supports the crest to crest definition.

Why Other Options Are Wrong:
Option B, from crest to nearest trough, is only half of a wavelength because it goes from maximum positive displacement to maximum negative displacement. Option C, from trough to crest, is also half a cycle and therefore does not give the full wavelength. Option D claims that none of the methods is correct, but physics textbooks clearly define wavelength using distances such as crest to crest, trough to trough, or any two equivalent phase points, so that statement is incorrect.

Common Pitfalls:
A common misunderstanding is to think that any two extreme points must represent one wavelength, so students mistakenly choose crest to trough. Another pitfall is confusing time period and wavelength, where students look along the time axis instead of the position axis. Some learners also mix wavelength with amplitude, even though amplitude measures height of the wave, not length of one cycle. Keeping the phrase distance between two consecutive crests in mind helps avoid these mistakes.

Final Answer:
The correct choice is From one crest of the wave to the next crest, because that distance represents one full spatial cycle of the periodic wave and matches the formal definition of wavelength.