(a) What is the ratio of the intensity of an earthquake wave as it passes a poin

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(a) What is the ratio of the intensity of an earthquake wave as it passes a point 20 km from the source to the intensity as it passes a point 15 km from the source?

 
(b) What is the ratio of the amplitude of an earthquake wave as it passes a point 20 km from the source to the amplitude as it passes a point 15 km from the source?

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Explanation & Answer

If we assume the energy spreads out equally in all directions, the intensity obeys the inverse square law.
(a) Distance increases by a factor of 20/15 = 1.33
Intensity reduces by 1.33² = 1.77
Ratio of intensities is 1/1.77 =0.56
(b) The intensity is proportional to amplitude squared, so amplitude is proportional to the square root of intensity. √1.77 = 1.33
Ratio of amplitudes is 1/1.33


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