The signal would only travel at the speed of sound in ping-pong balls. What that is precisely is very difficult to estimate. Try "wave propagation in granular m

The signal would only travel at the speed of sound in ping-pong balls. What that is precisely is very difficult to estimate. Try "wave propagation in granular materials" for a Googleable phrase. Even the case of a perfectly aligned 1-D chain of ideal ping-pong balls is not straightforward to analyze; the confinement force probably has a significant effect. (disclaimer: not a physicist)