Hearing damage may occur when a person is exposed to a sound intensity level of

Question

Hearing damage may occur when a person is exposed to a sound intensity level of 90.0 dB (relative to the threshold of human hearing) for a period of 9 hours. An eardrum has an area of 1.48 x 10^-4 m^2. How much sound energy is incident on the eardrum during this time? Hearing damage may occur when a person is exposed to a sound intensity level of 90.0 dB (relative to the threshold of human hearing) for a period of 9 hours. An eardrum has an area of 1.48 x 10^-4 m^2. How much sound energy is incident on the eardrum during this time?

Explanation / Answer

Sound intensity level in dB assigned to sound intensity J is:
L = 10*log(J/Jo)
where Jo = 10^-12 W/m^2 is th threshold of hearing

Hence:
J = Jo*10^(L/10)
So the intensity of a 90dB sound is:
J = 10^-12 *10^(90/10) = 10^-3 W/m^2
Multiply by the eardrum area and you get the power input to it.
P = J*A
Multiply this by the time of exposure ((in seconds!) and you have the incident energy:
E = P*t = J*A*t
= 10^-3*1.48*10^-4*9*3600
= 4.79*10^-3 J

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