108. Richter scale By what factor must the amplitude of an earthquake change to increase its severity by 1 point on the Richter scale? Assume that the period remains constant. The Richter scale is given by $R = \log \frac{A}{P}$ where A is the amplitude and P the period of the tremor.
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Then $R_2 = R_1 + 1$. Let $A_1$ be the initial amplitude and $A_2$ be the amplitude after the change. The Richter scale is given by $R = \log \frac{A}{P}$, where A is the amplitude and P is the period. Since the period remains constant, we can write: $R_1 = \log Show more…
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By what factor must the amplitude of an earthquake change to increase its severity by 1 point on the Richter scale? Assume that the period remains constant. The Richter scale is given by $$R=\log \frac{A}{P}$$ where $A$ is the amplitude and $P$ the period of the tremor.
Exponential and Logarithmic Functions
Properties of Logarithms
The Richter magnitude scale is logarithmic, meaning that each increase of 1 point on the scale corresponds to an increase by a factor of 10 in the amplitude of the seismic waves recorded on a seismograph. part A. An earthquake that measures magnitude 10 on the scale has how many times more ground-shaking effect than a quake that measures magnitude 5? Express your answer using one significant figure.
Shadi I.
The Richter scale is a logarithmic scale that expresses the magnitude of an earthquake. Each whole number increase in magnitude represents a tenfold increase in measured amplitude. For example, if the energy released by one earthquake was 750 times greater than the amount of energy released from another, you could solve the equation 10^x = 750 for x to find the difference in magnitude of the two quakes. To the nearest thousandth, find the difference in magnitude.
Joseph D.
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