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

Answer:

1

Step-by-step explanation:

       Magnitude $M$ of an earthquake is defined as $M=log\text{ }\frac{I}{S}$. 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 = $M\text{ = }log\text{ }\dfrac{I}{S}\text{ = }log\text{ }\dfrac{10S}{S}\text{ = }log\text{ }10\text{ = }log_{10}\text{ }10\text{ = }1$

∴ Magnitude of the earthquake is 1.