Hearing damage may occur when a person is exposed to a sound intensity level of 90.0 dB (relative to the threshold of hearing) for a period of 9.0 hours. One particular eardrum has an area of 1.90 10-4 m2. How much sound energy is incident on this eardrum during this time?

Answer 1

Sound intensity level in dB assigned to sound intensity J is:
L = 10 ∙ log₁₀(J/J₀)
where J₀ = 10⁻¹²W/m² is th threshold of hearing

Hence:
J = J₀ ∙ 10^(L/10)

So the intensity of a 90dB sound is:
J = 10⁻¹²W/m² ∙ 10^(90/10) = 10⁻³W/m²

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 ∙ 1.9 ∙10⁻⁴ ∙ 9 ∙3600 =
= 6.15•10⁻³J