- #1
Northbysouth
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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/IO) where is the sound intensity level,
IO = 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/IO)
I = IO10/10
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/m2
E = 17.5 μJ
Part B is where I'm stuck; I'm pretty sure it should be
Ke = 0.5*m*v2
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?