Question

For recording, we need sound of 50 dB at 2m from a speaker. What power output is required?

• A. $4.8\times {10}^{-6}W$
• B. $2.4\times {10}^{-6}W$
• C. $3.2\times {10}^{-6}W$
• D. $5.4\times {10}^{-6}W$

Answer 1

The correct option is A $4.8\times {10}^{-6}W$

$I=\frac{P}{4\pi r^2}$

$\text{/}50=\text{/}10lo{g}_{10}\frac{I}{{10}^{-12}}$

$5=lo{g}_{10}I+12lo{g}_{{10}^{10}}$

$⟹-7=lo{g}_{10}I$

$\therefore I={10}^{-7}W/m^2$

$I=\frac{P}{4\pi r^2}={10}^{-7}W/m^2$

$⟹P=4\times \frac{22}{7}\times 4\times {10}^{-7}$

$\approx$ $16\times 3\times {10}^{-7}$

$=48\times {10}^{-7}$
$=4.8\times {10}^{-6}W$