Walker, Halliday & Resnick — Waves-I: Problem 22

22 A human wave. During sporting events within large, densely packed stadiums, spectators will send a wave (or pulse) around the stadium (Fig. 16-29). As the wave reaches a group of spectators, they stand with a cheer and then sit. At any instant, the width \( w \) of the wave is the distance from the leading edge (people are just about to stand) to the trailing edge (people have just sat down). Suppose a human wave travels a distance of 853 seats around a stadium in 51 s, with spectators requiring about 1.8 s to respond to the wave’s passage by standing and then sitting. What are (a) the wave speed \( v \) (in seats per second) and (b) width \( w \) (in number of seats)?