Two students hear the same sound and their eardrums receive the same power from

Question

Two students hear the same sound and their eardrums receive the same power from the sound wave. The sound intensity at the eardrums of the first student is 0.58 W/m^2, while at the eardrums of the second student the sound intensity is 1.2 times greater. What is the ratio of the diameter of the first student's eardrum to that of the second student? If the diameter of the second student's eardrum is 0.95 cm, how much acoustic power, in microwatts, is striking each of his (and the other student's) eardrums?

Explanation / Answer

I1 = 0.58 W/m^2, I2 = 1.2*0.58 W/m^2

(a) Intensity = Power/Area

I2/I1 =d1^2/d2^2

12 = (d1/d2)^2

d1/d2 = 1.09

(b) d2 = 0.95 cm

I = P/A = P/(pi*d^2)

1.2*0.58= P/(3.14*0.0095^2)

P = 0.000197 W

P 1.97*10^-4 W

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