Question

The intensity of an earthquake with a magnitude of 2 is how many times greater than the intensity of an a standard earthquake ?

Answer 1

The intensity of an earthquake with a magnitude of 2 is 100 times greater than the intensity of a standard earthquake.

Explanation:

The magnitude of earthquakes is given by

`Magnitude=log(I)/(S)`

`2=log(I)/(S)\\`

Where I is the intensity of earthquake and S is the intensity of standard earthquake.

The magnitude of standard earthquakes is given by

`Magnitude=log(S)/(S)= log(1) = 0`

So comparing the magnitude of the given earthquake and standard earthquake,

`log(I)/(S) = log(S)/(S)`

`log(I)/(S) - log(S)/(S)`

`log(2) - log(1)`

`2 - 0`

`2`

which means that

`10^2 = 100` times greater

Therefore, the intensity of an earthquake with a magnitude of 2 is 100 times greater than the intensity of a standard earthquake.