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$\bullet$ Human hearing. A fan at a rock concert is 30 $\mathrm{m}$ from the stage, and at this point the sound intensity level is 110 $\mathrm{dB}$ . (a) How much energy is transferred to her eardrums each second? (See the previous problem.) (b) How fast would a 2.0 $\mathrm{mg}$ mosquito have to fly to have this much kinetic energy? Compare the mosquito's speed with that found for the whisper inpart (a) of the previous problem.

a) $E=5.54 \times 10^{-6} \mathrm{J}$b) $v=2.35 \times 10^{3} \mathrm{mm} / \mathrm{s}$The mosquito in this problem is 31756 times faster than the mosquito in Problem 16.13

Physics 101 Mechanics

Chapter 12

Mechanical Waves and Sound

Periodic Motion

Mechanical Waves

Sound and Hearing

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So we're told a fan at a rock concert is 30 meters from the stage, and at this point, the sound level. The sound intensity level is 110 decibels. We want to know how much energy is transferred to her ear drums. Second. Okay, well, we have a distance, a sound intensity level. And from the previous problem, we know that the diameter of the year is 8.4 millimeters. So we can sound intensity level and invert that equation and find the sound intensity. And we get a sound intensity 10 times 10 to the minus 12 times 10 to the power sound intensity level over 10. And that is 11. The coffee exponents. So we get us out. Intensity, uh, 1/10 watt per meter squared. Now the power her year is just that sound intensity pats the area cross sectional area. You're here. So we can I figured that out by pile before the square, and we wind up with 5.54 times 10 to the minus six watts. And if that's a constant than the the energy, the energy over one second, it's just power. Times one second, which gives US 5.54 times 10 minus six Jules. But then and asked, um, how fast would a two milligram mosquito have to fly to have this much kinetic energy? Well, we know the kinetic energy. Yes, the same is the energy. Coming to the ear is 5.54 times 10 to the minus six jewels. And the kinetic energy is 1/2 the mass of the mosquito. Times velocity Fine. So you can invert that we get the velocity that flying is the square root of two times the kinetic energy divided by its mass kinetic energy. You would give it up here, given its mass to be too milligrams. So that is two times tended my six gram, and we get 2.35 meters per second, which is extremely fast rumors, Tito.

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