Question

7. Attendance at this year’s Super Bowl is expected to be 72,000 spectators. Let’s assume that 80% of those fans are cheering for the Philadelphia Eagles, while the remaining fans (20%) are supporting the New England Patriots. On average, a single fan of either team will generate 50. dB of noise at field level when they cheer (or boo). Ignoring reflected sound waves, find the sound intensity (in both W/m2 and dB) when a) all the fans cheer, b) all the Eagles fans cheer, and c) all the Patriots fans cheer.Explain how you got your answer.

Answer 1

let I is the intensity of sound produced by each fan

beta = 10*log(I/Io)

50 = 10*log(I/10^-12)

5 = log(I/10^-12)

10^5 = I/10^-12

I = 10^-7 W/m^2

a) I_all the fans = 72000*I

= 72000*10^-7

= 0.0072 W/m^2

sound intensity level, beta_allthe fans = 10*log(I_all/Io)

= 10*log(0.0072/10^-12)

= 98.6 dB

b)

I_Eagels = 0.8*72000*I

= 57600*10^-7

= 0.00576 W/m^2

sound intensity level, beta_Eagles = 10*log(I_all/Io)

= 10*log(0.00576/10^-12)

= 97.6 dB

c) I_Patroits = 0.2*72000*I

= 14400*10^-7

= 0.00144 W/m^2

sound intensity level, beta_Patroits = 10*log(I_all/Io)

= 10*log(0.00144/10^-12)

= 91.6 dB