A human wave. During sporting events within large, densely packed stadiums, spec

Question

A human wave. During sporting events within large, densely packed stadiums, spectators will send a wave (or pulse) around the stadium (the figure). 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 876 seats around a stadium in 37.8 s, with spectators requiring about 1.90 s to respond to the wave's passage by standing and then sitting. What are (a) the wave speed v and (b) width w?

Explanation / Answer

(a) wave speed, v = (876/37.8) seat/sec = 23.17 seat/sec

(b) width, w = (v×1.9) = (23.17 × 1.90) seats

= 44 seats

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