The magnitude of an earthquake with intensity I is measured using a seismograph. The intensity I is converted into the Richter scale number using the following formula R=log10I. An earthquake in Town A was measured 3 on the Richter scale, while the earthquake in Town B measured 5 on the Richter scale. Let IA and IB be the intensity of the earthquakes in Town A and B respectively. What is the value of IBIA?
A seismograph 300 km from the epicenter of an earthquake recorded a maximum amplitude of 5.9 cross product 102µm. Find this earthquake's magnitude
To find the value of IBIA, we need to understand the relationship between intensity and the Richter scale.
According to the given information, the Richter scale measures the magnitude of an earthquake. It is calculated using the formula R = log10(I), where R is the Richter scale number and I is the intensity of the earthquake.
From the question, we are given that an earthquake in Town A has a Richter scale number of 3, and an earthquake in Town B has a Richter scale number of 5. Let's denote the intensity of the earthquakes in Town A and Town B as IA and IB, respectively.
Given that R(A) = 3 and R(B) = 5, we can set up the equations as follows:
R(A) = log10(IA) -- Equation 1
R(B) = log10(IB) -- Equation 2
To find the value of IBIA, we need to find the ratio of intensity in Town B to the intensity in Town A (IB/IA).
To do that, we can rearrange Equation 1 and Equation 2:
IA = 10 ^ R(A)
IB = 10 ^ R(B)
Substituting the given Richter scale values into these equations:
IA = 10 ^ 3
IB = 10 ^ 5
Calculating these values:
IA = 1000
IB = 100000
Now, we can find the value of IB/IA:
IBIA = IB / IA
= 100000 / 1000
= 100
Therefore, the value of IBIA is 100.