Question

A 58-dB sound wave strikes an eardrum whose area is 5.0×10−5m2. The intensity of the reference level required to determine the sound level is 1.0×10−12W/m2. 1yr=3.156×107s.

Part A: How much energy is absorbed by the eardrum per second?

Part B: At this rate, how long would it take the eardrum to receive a total energy of 1.0 J?

Answer 1

Hearing threshold = I₀ = 1 x 10^-12 W/m²

Sound level of the sound wave striking the eardrum = = 58 dB

Sound intensity striking the eardrum = I

I = 6.31 x 10^-7 W/m²

Area of the eardrum = A = 5 x 10^-5 m²

Energy absorbed by the eardrum per second = P

P = IA

P = (6.31x10^-7)(5x10^-5)

P = 3.155 x 10^-11 J/s

Time taken to receive a total energy of 1 J = t

Total energy received = E = 1 J

E = Pt

1 = (3.155x10^-11)t

t = 3.17 x 10¹⁰ sec

Converting time from seconds to years, (1 year = 3.156 x 10⁷ sec)

t = 1004.4 years

A) Energy absorbed by the eardrum per second = 3.155 x 10^-11 J/s

B) Time the eardrum will take to receive a total energy of 1 J = 1004.4 years