We have performed measurements on one-dimensional (1D) arrays of under
damped Josephson junctions connected in parallel by superconducting wi
res which in a magnetic field show resonances in the current-voltage c
haracteristics. From analytical calculations, we find that the positio
n of the steps is determined by the dispersion relation omega(k) of a
ID discrete, linear transmission line, where the Josephson junction ha
s been replaced by the capacitor and the resistance of the junction. W
hen nearest-neighbor inductances are accounted for, the model agrees w
ell with the measured positions of the steps. Numerical calculations o
f the full dynamics with inclusion of inductances between all cells su
pport our model. As an example of a system with a more complicated dis
persion, we have measured 1D arrays with two different junctions per p
rimitive cell. The measured dispersion relation shows an acoustic and
an optical branch in agreement with numerical simulations of the full
dynamics.