Question

A woman stands a distance d from a loud motor that emits sound uniformly in all directions. The sound intensity at her position is an uncomfortable 3.7×10-3 W/m2. At a distance 3.1 times as far from the motor, what are (a) the sound intensity and (b) the sound intensity level relative to the threshold of hearing? (a) Number Units (b) Number Units

Answer 1

Answer:

(a). The sound intensity is $0.385\times10^{-3}\ W/m^2$.

(b). The sound intensity level relative to the threshold is 85.85 dB.

Explanation:

Given that,

Sound intensity $I=3.7\times10^{-3}\ W/m^2$

Distance $r_{2}= 3.1r_{1}$

We know that the sound intensity

$Intensity\propto\dfrac{1}{distance^2}$

$I\propto\dfrac{1}{r^2}$

We need to calculate the sound intensity

Using relation of intensity

$\dfrac{I_{2}}{I_{1}}=\dfrac{r_{1}^2}{r_{2}^2}$

$I_{2}=\dfrac{r_{1}^2}{r_{2}^2}\times I_{1}$

Put the value into the formula

$I_{2}=3.7\times10^{-3}\times(\dfrac{r_{1}}{3.1r_{1}})^2$

$I_{2}=3.7\times10^{-3}\times(\dfrac{1}{3.1})^2$

$I_{2}=0.385\times10^{-3}\ W/m^2$

(b). We need to calculate the sound intensity level relative to the threshold

Using formula of sound intensity level

$L=10 log_{10}(\dfrac{I}{I_{0}})$

Put the value into the formula

$L=10 log_{10}(\dfrac{0.385\times10^{-3}}{10^{-12}})$

$L=85.85 dB$

Hence, (a). The sound intensity is $0.385\times10^{-3}\ W/m^2$.

(b). The sound intensity level relative to the threshold is 85.85 dB.