- #1

- 249

- 1

## Homework Statement

A fan at a rock concert is 35.0 m from the stage, and at this point the sound intensity level is 115 dB . 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 mm 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?

C) How fast a typical 2.0 {\rm mg} mosquito would have to fly mm/s to have an amount of energy delivered to the eardrum each second when someone whispers 20 dB a secret in your ear?

D) Compare the mosquito's speeds found in parts (B) and (C).

Please enter your answer as a number (factor) without the units.

## Homework Equations

Area of a circle = pi*r^2

β = 10log(I/I

_{O}) where is the sound intensity level,

I

_{O}= 10^-12

I = intensity per unit area = P/A where P is power and A is the surface are

K =0.5*m*v^2

## The Attempt at a Solution

I was able to answer part A by doing the following:

β = 10log(I/I

_{O})

I = I

_{O}10

^{/10}

I = (10

^{-12}W/M^2)*10

^{(115/10})

I = 0.326228 W/M^2

Then, knowing the intensity per unit area I multiplied the I by the surface area of the eardrum, which is

pi*(0.00420 m)

^{2}*0.316228 W/m

^{2}

E = 17.5 μJ

Part B is where I'm stuck; I'm pretty sure it should be

K

_{e}= 0.5*m*v

^{2}

Thus I have:

v = sqrt(2*(0.0000175246 kgm^2/s^2)/0.002 kg)

v = 0.13238 m/s

But the system doesn't accept it. So, what silly mistake am I making?