When one person shouts at a football game, the sound intensity level at the center of the fi eld is 60.0 dB. When all the people shout together, the intensity level increases to 109 dB. Assuming that each person generates the same sound intensity at the center of the fi eld, how many people are at the game?

The number of people at the game is 79433

Explanation:

[D] = 10 log (I/I₀)

I₀ = 10⁻¹² W/m²

D is sound intensity level in decibels

For a single person,

60 = 10 log (I/I₀)

6 = log (I/I₀)

10⁶ = (I/I₀)

I = I₀ * 10⁶

I = 10⁻¹² * 10⁶ = 10⁻⁶ W/m²

For all the people,

109 = 10 log (I/I₀)

10.9 = log (I/I₀)

10¹⁰•⁹ = (I/I₀)

I = I₀ * 10¹⁰•⁹

I = 10⁻¹² * 10¹⁰•⁹ = 10⁻¹•¹ W/m²

How many people in the stadium = (Total sound intensity level of all the people) / (sound intensity of one person)

Number of people in the stadium = (10⁻¹•¹) / (10⁻⁶) = 79432.8 = 79433 people.