Question

A fan at a rock concert is 30 m from the stage, and at this point the sound intensity level is 110 dB.How much energy is transferred to her eardrums each second? (Assume eardrum to be circular with a radius of 10mm)

• A. $\pi \times {10}^{-5}\frac{J}{S}$
• B. $2\pi \times {10}^{-5}\frac{J}{S}$
• C. $0.1\frac{J}{S}$
• D. None of these

Answer 1

The correct option is A

$\pi \times {10}^{-5}\frac{J}{S}$

$\beta =110dB$

$\beta =10log\left(\frac{I}{I_0}\right)\Rightarrow \frac{110}{10}=lo{g}_{10}\left(\frac{I}{{10}^{-12}}\right)$

${10}^{11}\times {10}^{-12}=I$

$I=0.1\omega m^{-2}$

Area of ear drum = $\pi (10\times {10}^{-3}{)}^2$

Energy supplied to ear in one second

= intensity $\times$ area of ear drum

=$0.1\times \pi \times {10}^{-4}$

=$3.14\times {10}^{-5}\frac{J}{S}$