Question

EARTHQUAKES The Richter scale magnitude reading m is given by m = log10 x, where x represents the amplitude of the seismic wave causing ground motion.

Determine the reading of an earthquake that is 10 times less intense than an earthquake that measures 4.5 on the Richter scale.

Answer 1

An earthquake that measures 4.5 on the Richter scale has an amplitude x of:

x = 10^(4.5)

x = 31,622.777

An earthquake that is 10 times less intense than this has an amplitude of:

x' = x/10

x' = 3,162.278

To find the Richter scale magnitude reading m' for this earthquake, we use the formula:

m' = log10(x')

m' = log10(3,162.278)

m' = 3.5

Therefore, the reading of the earthquake that is 10 times less intense than an earthquake that measures 4.5 on the Richter scale is 3.5 on the Richter scale.