Question

A sound wave with intensity 1.6×10−3 W/m2 is perceived to be modestly loud. Your eardrum is 6.0 mm in diameter. How much energy will be transferred to your eardrum while listening to this sound for 1.0 min?

Answer 1

Answer:

Energy  transferred to eardrum while listening to this sound for 1.0 min is $2.713 * 10^{-6}$

Explanation:

Given

Sound waves of intensity $1.6 * 10^{-3} \frac{W}{m^2}$

Size of the ear drum i.e diameter  $6.0$ millimeter

Radius of the ear drum

$= \frac{D}{2} \\= \frac{6}{2} \\= 3$

Time for which the eardrum will listen to this sound $= 1.0$ minutes.

As we know that the energy transferred to eardrum can be calculated by using below given relation

$E = I * A* t$

Where is the energy in Joules

I is the intensity in $\frac{W}{m^2}$

A is the area in $m^2$

and t is the time in seconds

Substituting the given values in above equation we get

$E = 1.6 * 10^{-3} * (\pi r^2)* 60\\E = 1.6 * 10^{-3} * (3.14 * (3*10^{-3})^2)* 60\\E = 2.713 * 10^{-6}$

Energy  transferred to eardrum while listening to this sound for 1.0 min is $2.713 * 10^{-6}$