A mismatched wavelength is rejected by arithmetic. Exact arithmetic here means exact results for the stated model inputs; measured inputs still carry uncertainty and significant-figure limits.

highlighted = computed this step

A wavelength label does not make a mode fit

Mode index 5 and wavelength 5 meters give 25 meters.

nλ=55=25 mn\lambda=5\cdot 5=25\ \mathrm{m}
Bad mode fitThe product misses the boundary condition.L=12 mn=5lambda=5 mfit=0nodes=6

The chain requires twice the length

Twice the chain length is 24 meters, so the fit bit is 0.

25 m24 m,fit=025\ \mathrm{m}\ne 24\ \mathrm{m},\quad fit=0
Rejected modeA false fit bit would fail validation.L=12 mn=5lambda=5 mfit=0nodes=6