Part A How much energy is delivered to the eardrum each second when someone whis

Question

Part A

How much energy is delivered to the eardrum each second when someone whispers (20.6dB ) a secret in your ear?
E = ________________________ J

Part B

To comprehend how sensitive the ear is to very small amounts of energy, calculate how fast a typical 1.10mg mosquito would have to fly (in mm/s) to have this amount of kinetic energy.
v = _________________________mm/s

Please show steps.. Thank you!!

Sound is detected when a sound wave causes the tympanic membrane (the eardrum) to vibrate (see the figure (Figure 1) ). Typically, the diameter of this membrane is about 8.40mm in humans Part A How much energy is delivered to the eardrum each second when someone whispers (20.6dB ) a secret in your ear? Part B To comprehend how sensitive the ear is to very small amounts of energy, calculate how fast a typical 1.10mg mosquito would have to fly (in mm/s) to have this amount of kinetic energy.

Explanation / Answer

We know that

I =Ps/4pir2-----(1)

but we know that ps =EOr w/t----(2)

The energy delivered to the eardrum is E =I*t*4pir2

Given that diameter d =8.40mm ===>r =d/2 =4.20*10-3m

t =1sec

I =20.6dB =1.148*10^-10W/m2

Now susbtitute the values we get E =2.54*10^-14J

Now KE =(1/2)mv2

velocity of the fly is v =SQrt(2KE/m) =Sqrt(2*2.54*10^-14/1.10*10^-3)=0.645*10^-5m/s=0.00625mm/s

  

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