A rock group is playing in a bar. Sound emerging from the door spreads uniformly in all directions. The intensity level of the music is 112 dB at a distance of 5.1 m from the door. At what distance is the music just barely audible to a person with a normal threshold of hearing? Disregard absorption. Answer in units of m.

Given Information:

distance = d₁ = 5.1 m

Intensity level of music = 112 dB

Required Information:

distance = d₂ = ?

distance = d₂ = 2030347 m

Explanation:  

We want to find out the distance where sound of music is barely audible to a person with normal threshold.

The intensity level of sound is  given by

Where I₀ = 10⁻¹²W/m² is the threshold level

eq. 1  

The intensity level and distance are inversely related  

I ≈ 1/d²  

The intensity of sound is 112 dB  at a distance of d1 = 5.1 m

We want to find the distance d2 where intensity of sound is 0 dB

 eq. 2

Substitute eq. 2 into eq. 1

Therefore, the required distance is d₂ = 2030347 m.