Answer to Question #288783 in Mechanics | Relativity for NICKO

Question

Sound is detected when a sound wave causes the tympanic membrane (the eardrum) to vibrate. Typically, the diameter of this membrane is about 8.4 mm in humans. (a) How much energy is delivered to the eardrum each second when someone whispers (20 dB) a secret in your ear? (b) To comprehend how sensitive the ear is to very small amounts of energy, calculate how fast a typical 2.0-mg mosquito would have to fly (in mm/s) to have this amount of kinetic energy

Answer 1

(a) The intensity of the 20dB-sound is

$$I=I_0·10^{(\beta/10)}=10^{-10}\text{ W/m}^2.$$

The area of the eardrum:

$$A=\dfrac14\pi d^2=5.67·10^{-5}\text{ m}^2.$$

The power is

$$I=PA=5.76·10^{-15}\text{ W}.$$

Each second, the energy is power times time:

$$E=Pt=5.76·10^{-15}\text{ J}.$$

(b) First, find the velocity:

$$v=\sqrt{2E/m}=7.59·10^{-2}\text{ mm/s}.$$