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Homework Help: Decibels, Waves, Kinetic Energy and Mosquitos

  1. Sep 11, 2012 #1
    1. The problem statement, all variables and given/known data
    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.

    2. Relevant 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

    3. 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?
  2. jcsd
  3. Sep 14, 2012 #2
    If you still need help with this question, you should double check your masses.

    The mass of the mosquito is given to us as 2.00 mg. You have the right equation KE=1/2mv^2 but the m needs to be in kg.

    Afterwards, solve for v like you were doing before.
  4. Sep 14, 2012 #3
    I have managed to solve this now and you're right about the masses. It should be:

    (17.5x10^-6) = 0.5*(2x10^-6)v^2

    Thus solving for v I get

    V = 4.19 m/s

    I mistook 2.00 mg to be equal to 0.002 kg which was a silly mistake to make.

    Thanks for your input.
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