Question

When one person shouts at a football game, the sound intensity level at the center of the field is 69.6 dB. When all the people shout together, the intensity level increases to 103 dB. Assuming that each person generates the same sound intensity at the center of the field, how many people are at the game

Answer 1

there are 2188 people at the game

Explanation:

Given the data in the question;

we know that decibel is defined as; dB = 10log(l/l₀)

so if one produces an intensity l₁, it results in 69.6 dB

69.6 = 10log(l₁/l₀) ---- equ1

also. if x number of people produces this intensity, it result to 103 dB

103 = 10log(xl₁/l₀)

103 = 10( log(l₁/l₀) + log(x) )

103 = 10log(l₁/l₀) + 10log(x) ----- equ2

input equation 1 into to equation 2

103 = 69.6 + 10log(x)

10log(x) = 103 - 69.6

10log(x) = 33.4

divide both side by 10

log(x) = 3.34

x =
`10^(3.34)`

x = 2187.76 ≈ 2188

Therefore, there are 2188 people at the game