Who leads whom
● VERBATIM — examined word-for-wordThe particle nearer the source leads (it started first). On y–t graphs: whoever reaches the crest earlier leads — measure crest-to-crest, never at intersection points (a named examiner complaint). Cyclic equivalence: B leads A by φ ⇔ A leads B by 2π − φ ⇔ A leads B by −φ. Two separate y–x graphs = two different waves: the one further advanced in the travel direction leads by (Δx/λ)2π. y–t graphs always compare particles, never whole waves.
What this actually means
'Leads' means 'got there first'. On a single travelling wave, the particle closer to the source started oscillating earlier, so it leads.
On two y–t curves, the one whose crest occurs earlier leads. Measure crest to crest; intersection points are a named examiner complaint because both curves pass through them without it meaning anything.
Lead and lag are cyclic: B leading A by φ is the same statement as A leading B by 2π − φ. And two separate y–x graphs compare two different waves, not two particles: the wave further advanced in the travel direction leads.
Measuring phase offset at graph intersection points — measure crest to crest.
Prove it — watch it be true
- Pick P nearer the source and Q further away
- Read the who-leads indicator: P leads
- Watch the y–t curves: P's crest arrives earlier than Q's