The intensity of a particular earthquake wave is measured to be 9.0 ✕ 106 J/m2·s

Physics
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The intensity of a particular earthquake wave is measured to be 9.0 ✕ 106 J/m2·s at a distance of 52 km from the source.

(a) What was the intensity when it passed a point only 2.0 km from the source?
 J/m2·s
(b) What was the rate energy passed through an area of 5.0 m2 at 2.0 km?
 W
Apr 1st, 2015

(a) Using the inverse square law, we know that intensity I is proportional to 1/d^2, where d is distance.

Thus, in this case, I2 = I1 * 1/(d1/d2)^2 = 9E6 [J/m^2*s]/(2 [km]/52 [km])^2 = 6.084E9 [J/m^2*s]

You could also think of this as I(2km) = I*A(52km)/A(2km) = 9.0*10^6*4pi*(52^2)/(2^2) = 6.084E9 [J/m^2*s]

(b) Since I = P/A, where I is intensity, P is power, and A is area,

P = I*A = 6.084E9 [J/m^2*s] * 5 [m^2] = 30.42E9 [J/s]

Apr 1st, 2015

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