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 6 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 6 hours
J

(b) 104 dB for 1 hour
J

(c) Is OSHA's safety standard simply a measure of the amount of energy absorbed by the eardrum?
Y or N   

Explain.

Explanation / Answer

here,

diameter = d = 9.5 mm = 0.0095 m

area of ear = pi*r^2 = 3.14 * 0.0095^2
A = 2.833 * 10^-4 m^2

as :
dB = 10 * log( I / (10^-12) )

solving for Intensity ,I :

I = 10^(dB/10)*10^-12

also Energy can be written as ,

E = intensity * Area * time
E = 10^(dB/10)*10^-12 * A * T --------------(1)

Where,
A = area in m^2
T = time in s

CASE A:
dB = 94.0 dB
t = 6 hr = 21600 s

using eqn 1 we get :
E = 10^(94/10)*10^-12 * 2.833 * 10^-4 * 21600
E = 0.0154 J

CASE B :
dB = 104 dB
t = 1 hr = 3600 s

using eqn 1 we get :
E = 10^(104/10)*10^-12 * 2.833 * 10^-4 * 3600
E = 0.0256 J

CASE C:

Yes

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