  Searches for stochastic gravitational-wave backgrounds using pulsar timing
arrays look for correlations in the timing residuals induced by the background
across the pulsars in the array. The correlation signature of an isotropic,
unpolarized gravitational-wave background predicted by general relativity
follows the so-called Hellings and Downs curve, which is a relatively simple
function of the angle between a pair of Earth-pulsar baselines. In this paper,
we give a pedagogical discussion of the Hellings and Downs curve for pulsar
timing arrays, considering simpler analogous scenarios involving sound and
electromagnetic waves. We calculate Hellings-and-Downs-type functions for these
two scenarios and develop a framework suitable for doing more general
correlation calculations.
