Question

Intensity level 2 cm from a source of sound is 80 dB. If there is no loss of acoustic power in air and intensity of threshold hearing is ${10}^{-12}$ $W{m}^{-2}$ then, what is the intensity level at a distance of 40 cm from source?

• A. Zero
• B. 54 dB
• C. 64 dB
• D. 44 dB

Answer 1

The correct option is B

54 dB

$I\propto \frac{1}{r^2}$ $\Rightarrow$ $\frac{I_2}{I_1}$ = $\frac{r_1^2}{r_2^2}$ = $\frac{2^2}{(40{)}^2}$ = $\frac{1}{400}$ $\Rightarrow I_1$ = $400I_2$

Intensity level at point 1, $I_1$ = $10lo{g}_{10}\left(\frac{I_1}{I_0}\right)$

and Intensity level at point 2, $I_2$ = $10lo{g}_{10}\left(\frac{I_2}{I_0}\right)$

$\therefore I_1-I_2$ = $10log\frac{I_1}{I_2}$ = $10lo{g}_{10}\left(400\right)$

$\Rightarrow I_1-I_2$ = $10\times 2.602$ = $26$

$I_2$ = $I_1-26$ = $80-26$ = $54dB$