Types of Waves — Question 5

Question 5

A moving crowd wave can leave every participant in place

People in a row are spaced $.50\,\mathrm{m}$ apart. Each person begins one stand-and-sit motion $.25\,\mathrm{s}$ after the previous person, progressing to the right. No participant walks along the row.

1. Find the speed of the coordinated pattern.

2. Distinguish this pattern from passive energy transmission on an ideal rope. What supplies most of the energy of each participant?

Question 5 - Solution

A moving crowd wave can leave every participant in place

Method and mathematical working

Use the spacing and response delay to determine how fast the activation event advances. Then identify the physical source of each participant's mechanical work.$$\begin{aligned}v_{\mathrm{pattern}}&=\frac{\text{neighbor spacing}}{\text{neighbor delay}}.\\[4pt]t_j&=j(0.25\,\mathrm s),\quad x_j=j(0.50\,\mathrm m),\quad \frac{x_{j+1}-x_j}{t_{j+1}-t_j}=2.0\,\mathrm{m/s}.\end{aligned}$$

(a) Calculation and conclusion

The pattern advances one spacing per delay, giving $.50/.25=2.0\,\mathrm{m/s}$ to the right. The participants remain near fixed locations while their vertical motion forms the visible disturbance.

(b) Interpretation and limits

Each participant supplies substantial mechanical energy from their own muscles after responding to a cue. The analogy illustrates pattern motion without bulk transport, but it does not establish that the rising motion is powered by mechanical energy passed through neighboring participants as in a passive rope.

Physical check

The cue can transfer information without transferring all the energy needed to stand up. A resemblance to a wave does not make the crowd a passive elastic medium.