Question

At a distance 2.0 m from a localized sound source you measure the intensity level as 79 dB .How far away must you be for the perceived loudness to drop in half (i.e., to an intensity level of 69 dB )?

Answer 1

Answer:

6.32 m

Explanation:

Intensity of sound (I) is inversely proportional the distance to the source (d).

In decibels,

$\Delta \beta=10log\frac{I_1}{I_2}=10 log\frac{d_2^2}{d_1^2}\\\\\Rightarrow 79-69=10 log\frac{d_2^2}{2^2}\\\Rightarrow 10 = 10 log\frac{d_2^2}{4}\\ \Rightarrow d_2^2=4\times 10\\\Rightarrow d_2=6.32 m$