Sign conventions flip graphs
Default: upward positive (transverse), rightward positive (longitudinal). If the question declares downward/leftward positive, the same motion plots as minus the default graph. Read the convention first; a sinusoidal y–t graph does NOT mean the wave is transverse — graph shape never reveals wave type.
What this actually means
Graphs are drawn against a declared positive direction. Flip the declaration and the same physical motion plots upside down. Nothing about the wave changed, only the bookkeeping.
First check on any unfamiliar graph: which direction is positive. Second check: never deduce wave type from graph shape. A longitudinal wave's displacements plot as a perfectly good sinusoid.
Assuming a sinusoidal graph means a transverse wave — graph shape never reveals wave type.
Prove it — watch it be true
- Flip the sign-convention toggle
- Watch the graph mirror while the beads move exactly as before
- Same physics, opposite plot — the convention is a choice, not a fact