A fan at a rock concert is 30.0 m from the stage, and at this point the sound in

Question

A fan at a rock concert is 30.0 m from the stage, and at this point the sound intensity level is 109dB. 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 mg mosquito would have to fly (in nm/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).

Explanation / Answer

a> sound intensity = 110 dB = 10-12 * 10110/10 = 0.1 J/m2

diameter = 8.4 mm

Energy transferred = 0.1 * * 8.42 * 10-6/ 4 = 5.542 * 10-6 J per second

b> 0.5 mv2 = 5.542 * 10-6

v2 = 5.542*10-6 * 2/ 2*10-6 = 5.542

v = 2.354 m/s

c> v2 = 5.542 * 10-15 * 2/2*10-6 = 5.542 * 10-9

v = 7.44 * 10-5 m/s = 0.0744 mm/s

d> vB /vC = [10(110 - 20)/10 ] = 31623

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