Question

"The wave" is a particular type of pulse that can

propagatethrough a large crowd gathered at a sports arena to watch
a socceror American football match. The elements of the medium
arespectators, with zero position corresponding to their being
seatedand maximum position corresponding to their standing and
raisingtheir arms. When a large fraction of the spectators
participate inthe wave motion, a somewhat stable pulse shape can
develop. Thewave speed depends on people's reaction time, which is
typically onthe order of 0.1s. Estimate the order of magnitude, in
minutes, ofthe time required for such a pulse to make one circuit
around alarge sports stadium. State the quantities you measure or
estimateand their values.

Answer 1

t = 36π seconds

Step-by-step explanation:

For resolving this problem, we are going to consider a representative stadium of the United States. The Mercedes-Benz Stadium located in Atlanta, Georgia has an average radius of 90 m.

Then, its circumference measures:

L = 2πr

L = 2π(90)

L = 180π m

First, we estimate the wave's velocity: the average width of an person is 0.5 m, then the velocity is:

v = x/t

Where x: person's width

t: time

v = 0.5/0.1 = 5 m/s

The time required for the pulse to make one circuit around the stadium is:

t = x/v = 180π/5 = 36π seconds