OSHA, the Occupational Safety and Health Administration, has established shandar

Question

OSHA, the Occupational Safety and Health Administration, has established shandards for workplace exposure to noise. According to OSHA's Hearing Conservation Standard, the permissible noise exposure per day is 94.0 dB for 5 hours or 104 dB for 1 hour. Assuming the eardrum is 9.5 mm in diameter, find the energy absorbed by the eardrum, when subjected to each of these conditions.

(a) 94.0 dB for 5 hours

(b) 104 dB for 1 hour

(c) Is OSHA's safety standard simply a measure of the amount of energy absorbed by the eardrum? Yes or no?

Explanation / Answer

A) (a) 94.0 dB for 5 hours

Area = 3.14*d ( given d=9.5 mm)

Area=3.14*9.5*10^-3 m^2

First convert 94 dB to intensity I using Beta = 10db*log(I/10^-12)
So I = 10^(94/10)*10^-12 = 2.51x10^-3W/m^2

So the energy = I*A = 2.51x10^-3*3.14*9.5*10^-3 = 7.48x10^-5W Which is 7.48x10^-5J per second

so in 5 hour energy absorbed= 18000*7.48x10^-5 =1.34 w

b) 104 dB for 1 hour

First convert 104 dB to intensity I using Beta = 10db*log(I/10^-12)
So I = 10^(104/10)*10^-12 = 0.0251 W/m^2

So the energy = I*A = 0.0251 *3.14*9.5*10^-3 = 7.48x10^-4W Which is 7.48x10^-4J per second

so in 1 hour energy absorbed= 3600*7.48x10^-4 =2.69 w

3) Yes

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