Question

What is the ratio of the intensities and amplitudes of an earthquake P wave passing through the Earth and detected at two points 27 km and 13 km from the source?
(a) I 27 / 13 =__________
(b) A 27 / 13 =_____________-

Answer 1

For both cases we will use the proportional values of the distance referring to the amplitude and intensity. Theoretically we know that the intensity is inversely proportional to the square of the distance, while the amplitude is inversely proportional to the distance, therefore,

PART A )  Intensity is inversely proportional to the square of the distance

$Intensity \propto \frac{1}{distance^2}$

Therefore the intensity of the two values would be

$\frac{I_{27}}{I_{13}} = \frac{(13km)^2}{(27km)^2}$

$\mathbf{\therefore \frac{I_{27}}{I_{13}} = 0.232 }$

PART B) Amplitude is inversely proportional to the distance

$Amplitude \propto \frac{1}{distance}$

$\frac{A_{27}}{A_{13}}= \frac{(13km)}{(27km)}$

$\mathbf{\therefore\frac{A_{27}}{A_{13}}= 0.4815}$