Question

The magnitude, M, of an earthquake is defined to be M=log I/S, where I is the intensity of the earthquake (measured by the amplitude of the seismograph wave) and S is the intensity of a “standard” earthquake, which is barely detectable. What is the magnitude of an earthquake that is 10 times more intense than a standard earthquake? Use a calculator. Round your answer to the nearest tenth.

Answer 1

1

Explanation:

Magnitude
`M` of an earthquake is defined as
`M=log\text{ }(I)/(S)`. Here
`I` is the Intensity of the earthquake and
`S` is the intensity of standard earthquake.

We have an earthquake that is 10 times more intense than a standard earthquake. Let us denote the intensity of the earthquake as
`I`.

10 times more intense than standard earthquake ⇒
`I=10S`

Magnitude of the earthquake =
`M\text{ = }log\text{ }(I)/(S)\text{ = }log\text{ }(10S)/(S)\text{ = }log\text{ }10\text{ = }log_(10)\text{ }10\text{ = }1`

∴ Magnitude of the earthquake is 1.