Calculating Wave Velocity in a Stadium

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SUMMARY

The discussion focuses on calculating wave velocity in a circular stadium using the formula v = 2π(a + nd)/T, where v represents wave velocity, T is the period, a is the distance to the first row, d is the distance between rows, and n is the row number. The angular frequency w is defined as w = 2π/T. Participants are encouraged to explore the elliptical case for further understanding. This mathematical approach is essential for analyzing human wave dynamics during football games.

PREREQUISITES
  • Understanding of wave mechanics and physics principles
  • Familiarity with circular geometry and its properties
  • Basic knowledge of trigonometric functions, specifically sine and cosine
  • Ability to manipulate algebraic equations and solve for variables
NEXT STEPS
  • Research the implications of wave velocity in different stadium shapes, particularly elliptical stadiums
  • Study the effects of varying row distances on wave propagation
  • Explore the relationship between wave period and frequency in physical systems
  • Investigate real-world applications of wave dynamics in sports and crowd behavior
USEFUL FOR

Physics students, sports event organizers, mathematicians, and anyone interested in crowd dynamics and wave phenomena in stadium settings.

flatmaster
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Football season's coming up, so here we go.

Assume a circular stadium. A "Human wave" travels around the stadium.
T = period
a = distance to first row
d = distance between rows
n = row number (may need to be converted from a letter or double letter)

Wave velocity

v = wr
v = w(a+nd)


or...

w=2pi/T

v = 2pi(a+nd)/T

It is left to the student to work out the elliptical case.
 
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