Calculating Wave Velocity in a Stadium

[flatmaster]

Football season's comming 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.

 

[adnan-ul-haq]

Nice info

 

[sir-pinski]

Great question! Calculating wave velocity in a stadium is definitely an interesting concept, especially with football season around the corner. The formula provided for wave velocity, v=2pi(a+nd)/T, is a great starting point. As the formula suggests, the velocity of the wave is dependent on the period of the wave, the distance from the first row of the stadium (a), the distance between rows (d), and the row number (n).

To calculate the wave velocity in a circular stadium, we can use the formula v=wr, where w is the angular velocity. To find the angular velocity, we can use the formula w=2pi/T, where T is the period of the wave. This will give us the velocity of the wave as it travels around the circular stadium.

However, for an elliptical stadium, the formula becomes a bit more complex and may require some additional calculations. The distance between rows and the row number (d and n) may need to be converted to account for the elliptical shape of the stadium. This can be done by using the stadium's eccentricity, which is the ratio of the distance between the center and one focus to the distance between the center and the corresponding vertex. With this information, we can adjust the formula to accurately calculate the wave velocity in an elliptical stadium.

Overall, calculating wave velocity in a stadium requires some mathematical calculations and considerations, but it is definitely a fascinating concept to explore. Thank you for bringing up this interesting topic and good luck with the upcoming football season!