Question

An earthquake in california measured 3.6 on the richter scale. use the formula r = log(lambda/lambda_{0}) to determine approximately how many times stronger the wave amplitude of the earthquake was than ao. a \approx 3, 981a_{0} a \approx 36.6a_{0} a \approx 0.56a_{0} a \approx 14, 332a_{0}

Answer 1

The Richter scale measurement of 3.6 indicates that the amplitude of the earthquake was approximately 3981 times stronger than the amplitude of a baseline earthquake.

Step-by-step explanation:

The Richter scale is a logarithmic scale used to measure the strength or energy released by an earthquake. An earthquake that measured 3.6 on the Richter scale uses the formula r = log(λ/λ_0), where r is the Richter scale measurement, λ is the wave amplitude of the earthquake, and λ_0 is the wave amplitude of a baseline earthquake. To determine how many times stronger the wave amplitude of this earthquake is compared to the baseline, we solve for λ/λ_0:

3.6 = log(λ/λ_0)
10^3.6 = λ/λ_0
λ/λ_0 ≈ 3981

Therefore, the correct answer is ≈ 3981λ_0, indicating the wave amplitude of the earthquake is approximately 3981 times stronger than the baseline.

Answer 2

The wave amplitude of the earthquake is approximately 398.107 times stronger than a0.

Step-by-step explanation:

To determine approximately how many times stronger the wave amplitude of the earthquake was than a0, we can use the Richter scale formula: r = log(lambda/lambda0). In this case, the Richter scale measurement is 3.6. The formula relates the ratio of the wave amplitude (lambda) of the earthquake to the reference wave amplitude (lambda0).

By rearranging the formula, we can solve for lambda: lambda = lambda0 * 10r.

Substituting r = 3.6 and lambda0 = 1, we get: lambda = 1 * 103.6. Evaluating the expression gives us lambda ≈ 398.107.

Therefore, the wave amplitude of the earthquake is approximately 398.107 times stronger than a0.