Question

An earthquake near New Zealand measured 4.2
on the Richter scale. Use the formula r=log(a/a0)
to determine approximately how many times stronger the wave amplitude of the earthquake was than A0
.
a. a=15,849 A0
b. a=0.62 A0
c. a=66,566 A0
d. A=66.7 A0

Answer 1

Use r = log10(a/a0). So a/a0 = 10^r = 10^4.2 = 10^4 * 10^0.2 = 10000 * 1.584893… ≈ 15,849.
Answer: (a) a = 15,849 A0.