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

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 =

x = 2187.76 ≈ 2188

Therefore, there are 2188 people at the game

d₁ = displacement of tern from arctic to antarctic = 11000 miles

d₂ = displacement of tern from antarctic to arctic =   - 11000 miles

d = total displacement for the journey

total displacement for the journey is given as

d = d₁ + d₂

d = 11000 + (-11000)

d = 0 miles

t₁ = time of travel from arctic to antarctic = 3 months = 3 x 30 days = 90 days

t₂ = time of travel from antarctic to arctic = 3 months = 3 x 30 days = 90 days

t = total time of travel

total time of travel is given as

t = t₁ + t₂

t = 90 + 90

t = 180 days

average velocity is given as

average velocity = total displacement/ total time

v = d/t

v = 0/180

v = 0 miles/day