7. Attendance at this year’s Super Bowl is expected to be 72,000 spectators. Let

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.

Explanation / Answer

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

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