Snapshot vs biography
● VERBATIM — examined word-for-wordDisplacement–distance: photo of ALL particles at one instant → read y₀ and λ; T is unreadable (use T = 1/f). Displacement–time: one particle tracked → read y₀ and T; λ unreadable. Same shape, different universe. Look at the axes before anything else — the school lecturer repeats this "like a broken recorder".
What this actually means
The two graphs look identical, both sinusoids, but answer different questions. The y–x graph freezes time: every particle photographed at one instant. The y–t graph freezes space: one particle tracked through time.
So a y–x graph hands you y₀ and λ but can never show T; a y–t graph hands you y₀ and T but can never show λ. Reading T off a distance axis is the most reliable way to throw away the first mark of a question.
Build the habit: read the axis labels before your eyes touch the curve.
Reading T off a y–x graph, or λ off a y–t graph — check axes first, every time.
Prove it — watch it be true
- Compare the y–x and y–t panels side by side: same shape
- Measure λ on the y–x panel and T on the y–t panel
- Try to find T on the y–x panel — you cannot, and that is the point