Question

'The wave' is a particular type of pulse that can propagate through a large crowd gathered at a sports arena to watch a soccer, hockey, or CFL game. The elemets of the medium are the spectators, with zero position corresponding to their being seated and maximum position corresponding to their standing and raising their arms. When a large fraction of the spectators participate in the wave motion, a somewhat stable pulse shape can develop. The wave speed depends on people's reaction time, which is typically on the order of 0,1s. Estimate the order of magnitude, in minutes, of the time required for such a pulse to make one circuit around BC Place Stadium in Vancouver.

State all the assumptions that you've made.

Information about BC Place: dimensions are approximately 100 m X 85 m.

Answer 1

The total time required is 1 minute and 0.3 seconds.

Assumption: The distance between the people is 1 m and the stadium is a circle with a radius of 100m.

Here, the time taken by the person is 0.1 seconds.

Total distance covered by the wave = Circumference of the circle

So, total distance = 2 πr = 2 × 3.14 × 100 = 618 m

As the distance between each of the people is 1 m.

So, the number of personal interactions is 618.

Time taken by each person is 0.1 seconds.

So, total time, t = 0.1 × 618 = 61.8 seconds.

So, the order of the magnitude of the time required is 1 minute and 0.3 seconds for such a pulse to make one circuit around BC Place Stadium in Vancouver.

Hence, the total time required is 1 minute and 0.3 seconds.

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