Question

If the maximum daily exposure at 97 dB is 3 hours, the maximum daily exposure at 105 dB is 1 hour, and the maximum daily exposure at 110 dB is 30 minutes, how many hours per day can a worker can a worker be exposed to 97 dB noise if she is exposed to 105 dB noise for 10 minutes and 110 dB noise for 10 minutes?

Answer 1

let A is the area of the ear drum.

let I1,I2 and I3 are the intensity of sound corresponding to 97dB, 105 dB and 110 dB.

we know, sound intensity level = 10*log(I/Io) dB

97 = 10*log(I1/10^-12)

9.7 = log(I1/10^-12)

10^9.7 = I1/10^-12

==> I1 = 10^(9.7-12)

= 0.00501 W/m^2

simillarly, I2 = 10^(10.5-12)

= 0.0316 W/m^2

I3 = 10^(11-12)

= 0.1 W/m^2

maximum Energy obsorbed by the ear = I1*A*t1 + I2*A*t2 + I3*A*t3

= 0.00501*A*(3*60*60) + 0.0316*A*(60*60) + 0.1*A*(30*60)

= 347.8*A J

now use

t2 = 10 min

t3 = 10 minues

t1 = ?

maximum energy that can be obsorbed = 0.00501*A*t1 + 0.0316*A*(10*60) + 0.1*A*(10*60)

347.8*A = 0.00501*A*t1 + 0.0316*A*(10*60) + 0.1*A*(10*60)

t1 = 53660 s

= 53660/(60*60)

= 14.9 hours/day