91Ó°ÊÓ

To calculate the distance required to move by the person by using the distance-intensity relation is $\frac{{\mathrm{r}}_1}{{\mathrm{r}}_2}=\sqrt{\frac{{\mathrm{I}}_2}{{\mathrm{I}}_1}}$were. $r_1$ is the initial distance. $r_2$is the final distance. $l_2$ is the final intensity of the sound. $l_1$ is the initial intensity of the sound.

The intensity of the sound at a distance 15.0 m apart is 20.0 dB.

Formula to calculate the difference of two sound intensity level is ${\mathrm{β}}_2-{\mathrm{β}}_1=10\log \left(\frac{{\mathrm{l}}_2}{{\mathrm{l}}_1}\right)$were, ${\mathrm{β}}_2$is the final intensity level of the sound. ${\mathrm{β}}_1$is the initial intensity level of the sound.

Substitute 60.0 dB for ${\mathrm{β}}_2$and 20.0 dB for ${\mathrm{β}}_1$in the above equation to find $\left(\frac{{\mathrm{l}}_2}{{\mathrm{l}}_1}\right)$

$$\begin{gathered} 60.0\mathrm{dB}=10\log \left(\frac{{\mathrm{l}}_2}{{\mathrm{l}}_1}\right) \\ \left(\frac{{\mathrm{l}}_2}{{\mathrm{l}}_1}\right)=40.0\mathrm{dB} \end{gathered}$$

Substitute 40.0dB for$\left(\frac{{\mathrm{l}}_2}{{\mathrm{l}}_1}\right)$ and 15.0m for $r_1$to find$r_2$

$$\begin{gathered} \frac{15.0\mathrm{m}}{{\mathrm{r}}_2}=\sqrt{40.0\mathrm{dB}} \\ =15.0\mathrm{cm} \end{gathered}$$

Therefore, the person is required to move 15.0 cm towards the direction of the conversation