Question

A fan at a rock concert is 40.0 mm from the stage, and at this point the sound intensity level is 108 dBdB . Sound is detected when a sound wave causes the tympanic membrane (the eardrum) to vibrate . Typically, the diameter of this membrane is about 8.40 mmmm in humans?(A) How much energy is transferred to her eardrums each second ?
(B) How fast would a 2.00 mg mosquito have to fly to have this much kinetic energy?

Answer 1

Answer with Explanation:

We are given that

Intensity level,L=108 dB

Diameter=$d=8.4 mm=8.4\times 10^{-3} m$

$1 mm=10^{-3} m$

a.$I_0=1.0\times 10^{-12}W/m^2$

$I=(10^{\frac{L}{10}})I_0$

Substitute the values

$I=(10^{\frac{108}{10}})(1.0\times 10^{-12})=0.063W/m^2$

Energy transferred to eardrums

$E=\frac{I\pi d^2}{4}=0.063\times \frac{\pi(8.4\times 10^{-3})^2}{4}=1.11\times 10^{-6} J$

B.Kinetic energy=$\frac{1}{2}mv^2$

Mass,m=2 mg=$2\times 10^{-6} Kg$

$1mg=10^{-6} kg$

$\frac{1}{2}mv^2=E$

$v^2=\frac{2E}{m}$

$v=\sqrt{\frac{2E}{m}}$

$v=\sqrt{\frac{2\times 1.11\times 10^{-6}}{2\times 10^{-6}}$

$v=1.05 m/s$