The Athletic Department at your school hosts a celebrity football game for which
ID: 1385391 • Letter: T
Question
The Athletic Department at your school hosts a celebrity football game for which no tickets are sold but cash donations are welcome and expected. Since tickets are not collected, they are looking for a creative manner to get a good estimate of the number of fans attending the event. Before the day of the game, you stand in the middle of the field and record the sound intensity level of a friend midway up in the stands as 51.2 dB. Before the game starts, the announcer asks for a big round of applause and appreciation for participating celebrities and you record the sound intensity level as87 dB. What is your estimate of the number of people attending the event?
Explanation / Answer
51.2 = 10 Log (Nx/N), where Log is the logarithm with basis 10, and Nx/N is a dimensionless quantity associated to the friend.
87 = 10 Log (Np/N) for the people characterized by Np. Thus, 87 - 51.2 = 10 Log(Np/Nx) => 3.58 = Log(Np/Nx) => 10^3.58 = Np/Nx => 3801= Np/Nx which tells us that the people attending the event is about 3800 individuals.
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