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* 10^(-3) m`

`1 mm=10^(-3) m`

a.
`I_0=1.0* 10^(-12)W/m^2`

`I=(10^{(L)/(10)})I_0`

Substitute the values

`I=(10^{(108)/(10)})(1.0* 10^(-12))=0.063W/m^2`

Energy transferred to eardrums

`E=(I\pi d^2)/(4)=0.063* (\pi(8.4* 10^(-3))^2)/(4)=1.11* 10^(-6) J`

B.Kinetic energy=
`(1)/(2)mv^2`

Mass,m=2 mg=
`2* 10^(-6) Kg`

`1mg=10^(-6) kg`

`(1)/(2)mv^2=E`

`v^2=(2E)/(m)`

`v=\sqrt{(2E)/(m)}`

`v=\sqrt{(2* 1.11* 10^(-6))/(2* 10^(-6))`

`v=1.05 m/s`