Lucas is working on a research to design a special loudspeaker that would transf

Question

Lucas is working on a research to design a special loudspeaker that would transfer sound energy to growing bald (like mine) in order to cure baldness. He believes that baldness can be cured by warming the scalp with sound waves. To test his first design, he asks me to sit underneath the bye-bye-bald loudspeakers, where my head is bathed with 93dB of soothing 800 Hz sound waves. Let's model my half-bald head as an 18-cm-diameter hemisphere. If he starts with 0.29J of sound energy as an appropriate "dose," how many minutes should my first therapy session last?

Explanation / Answer

we have intensity of waves = 93 dB

so 93 dB = 10 log ( I / (10^-12))

I = Intensity (in W/m^2) = 0.00199526 W/m^2

surface area of head = pi * d^2 = 3.14 * 0.18^2 = 0.101736 m^2

so rate at which energy is hoing to head = Intensity *area = 0.101736 *  0.00199526 = 0.000202989771 W

So for 0.29 J , time = energy/rate = 0.29/0.00020298977136 = 1428.64341 seconds = 23.81 minutes is the answer

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