Question

An 8 hour exposure to a sound intensity level of 90.0 dB may cause hearing damage. What energy in joules falls on a 0.500 cm diameter eardrum so exposed? ________J

Answer 1

Solution:- We know that I (dB) = 10 log (I/Io)

where, Io = 10^-12 W/m^2 —- Intensity just audible corresponds to 0 dB.

Now,

=> 90 = 10 log ( I/10^-12)

By multiplying 10^10 both sides and rearranging the equation,

I = 0.01 W/m^2

Now, Watt = Joules/second

and 8 hours = 28800 sec and Area = pie * r^2 => Area = 22/7 * (0.0025)^2 m^2 = 1.96 * 10^-5 m^2

( Given: d = 0.500 cm and time = 8 hours)

Sound Energy = Sound Intensity * time * Area

=> Sound Energy = 0.01* 28800 * 1.96 * 10^-5 = 0.00564 J

=> Sound Energy = 0.00564 J. Answer