Question

A 60-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. How much energy is absorbed by the eardrum per second?At this rate, how long would it take the eardrum to receive a total energy of 1.0 J?

Answer 1

Given,

A = 5 x 10^-5 m² ; I = 10^-12 W/m²

a)We know that Intensity in dB is

DB = 10 log (I/Io)

DB = 10 (log I - log Io)

DB/10 + log Io = log I

60/10 + log (10^-12) = log I

6.0-12 = log I

I = 10^-6W/m²

We know that, Intensity = Power / Area

Power = Intensity x Area = 10^-6 x 10^-0.2 x 5 x 10^-5 m² = 5* 10^-11 W

Hence, Energy per second = 5.0*10^-11 W

We know that, Power = Energy/Time

Time = Energy/Power = 1 J / 5.0 x 10^-11 W = 5.0*10^-11 s = 5.0*10^10 s/3.156 * 10^7 = 1584.28 years

Hence, T = 1584.28 years Answer

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