Standing waves & resonance (every paper)

Draw the harmonic; count loops; λ from the drawing, then v = fλ.

System	Fundamental	Harmonics
String both ends	λ = 2L	All n: λₙ = 2L/n
Open tube	λ = 2L	All n
Closed tube	λ = 4L	Odd n only

Resonance: driving frequency matches a natural frequency → large amplitude standing wave.

Exam-style String 0.60 m, third harmonic f = 240 Hz Find the wave speed. λ₃ = 2L/3 = 0.40 m v = fλ = 240 × 0.40 = 96 m s⁻¹ ✓ 96 m s⁻¹. The drawing of 3 loops earns the structure mark.

Reading a wave-crossing-a-boundary scenario (shallow to deep water)

Frequency stays FIXED (set by the source) as the wave crosses the boundary.
Wavelength and speed CHANGE together in the same direction — both increase, or both decrease, so v = fλ still balances.

Practice for this standard covers the whole topic — flashcards and quiz.