An earthquake near the Philippines measured 5.1 on the Richter scale. Use the formula R=log(A/a_0) to determine approximately how many times stronger the wave amplitude A of the earthquake was than A_0.
To calculate the ratio of wave amplitudes, we need to plug the values into the formula R=log(A/a_0) where R is the Richter scale value (5.1), A is the wave amplitude of the earthquake, and a_0 is the reference amplitude of 1.0 µm.
5.1 = log(A/1.0)
Now, we need to solve for A:
10^(5.1) = A
A ≈ 125.89 µm
Now we can determine how many times stronger the wave amplitude A of the earthquake was than A_0:
A/1.0 = 125.89/1.0 ≈ 125.89
Therefore, the wave amplitude of the earthquake was approximately 125.89 times stronger than the reference amplitude A_0.