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 93.0 dB for 4 hours or 103 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) 93.0 dB for 4 hours

(b) 103 dB for 1 hour

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

Answer 1

Given,

Diameter of ear drum=9.5mm

Area of ear drum,A==

A=7.09*10^-5 m2

a)93.0dB for 4 hours

Decibels are an expression of sound intensity (power/area) relative to a reference value.
Db = 10*log10(I/I0)

93=10*log(I/I0)

(I/10^-12)=10^(9.3)

I=1.99*10^-3 w/m2

Energy absorbed by ear drum per second,E=I*A=1.99*10^-3*7.09*10^-5=1.41*10^-7 J/s

Time duration for absorption in 4 hours

Therefore,Total energy absorbed,E1=E*T=1.41*10^-7*(4*60*60)=2.03*10^-3 J

b)103.0dB for 1 hours

Decibels are an expression of sound intensity (power/area) relative to a reference value.
Db = 10*log10(I/I0)

103=10*log(I/I0)

(I/10^-12)=10^(10.3)

I=6.76*10^-2 w/m2

Energy absorbed by ear drum per second,E=I*A=6.76*10^-2*7.09*10^-5=4.792*10^-6 J/s

Time duration for absorption in 1 hours

Therefore,Total energy absorbed,E1=E*T=4.792*10^-6*(1*60*60)=17.25*10^-3 J

C)No.It is the maximum number of hours per day a worker may be exposed to certain sound levels