SOLUTION: Two earthquakes differ by 1.0 when measured on the richter scale. How would the seismographic readings differ at a distance of 100 kilometers from the epicenter? How do their inten

Question 65623This question is from textbook Algebra & trigonometry
: Two earthquakes differ by 1.0 when measured on the richter scale. How would the seismographic readings differ at a distance of 100 kilometers from the epicenter? How do their intensities compare? This question is from textbook Algebra & trigonometry

Answer by stanbon(75887) (Show Source): You can put this solution on YOUR website!
Two earthquakes differ by 1.0 when measured on the richter scale. How would the seismographic readings differ at a distance of 100 kilometers from the epicenter? How do their intensities compare?
----------
Assume one of the earthquakes has magnitude M and the other has magnitude M+1.
Then M=10log(P/Po) where Po is the minimum detectable earthquake power.
Then M/10= log(P/Po)
Then P/Po=10^(M/10)
And P=Po[10^(M/10)]
Note: P is the Power of the earthquake whose Ricter measurement is M.
----------------
For the 2nd earthquake:
M+1=10log(P/Po)
(M+1)/10=log(P/Po)
P/Po=10^[(M/10)+1/10]
P=Po[10^(M/10}*(10^(1/10)
P=Po[10^(M/10)]*1.25
------------
So the 2nd earthquake is 1.25 times as powerful as the 1st.
That means the 2nd is 25% stronger than the 1st.
------------
Cheers,
Stan H.
RELATED QUESTIONS
I have no experiences using a logarithm so I need help trying to figure out how this... (answered by stanbon)

The Richter scale measures the energy released at the centre of an earthquake,... (answered by Theo)

The intensity levels I of two earthquakes measured on a seismograph can be compared by... (answered by Theo)

The intensity levels I of two earthquakes measured on a seismograph can be compared by... (answered by MathLover1)

I am horrible when it comes to word problems. I have been at this for two hours now and... (answered by prince_abubu)

The Richter scale measures the energy released at the centre of an earthquake,... (answered by Boreal)

Suppose that the regression equation y = 16.99 + 0.32 x1 + 0.41 x2 + 5.31 x3 predicts an... (answered by greenestamps)

In the last year, a total of 2749 earthquakes occurred in the country. Of... (answered by Cromlix)

If one earth quake has a magnitude of 5.2 on the Richter scale and a second earthquake... (answered by Boreal)