The Richtr scale was evied y Cahrles F.Richter a American geologist. The scale is based on the equation M(x)=logx/x0(little 0), where x is the seismographic reading of the earthquake and x0 i 1 miron 0.001mm (the seismographic reading of a zero-level earthuquake)
a) Determine the magnitude of an earthquake with a seismographic readin of 1 mm
b)It is true that an earthquake of magnitude 8 i twice as intense as an earthquake of magnitude 4? Explain
c) Express the equation M=logx/x0(little 0) in exponential form
d) An earthquake measuring 6.1 on the Richter cakeoccoedin Greece on June 15, 1955. Use your results form (c) above to determine its seismographic reading
Your "x0 i 1 miron 0.001mm"
is unintelligible. Please make sure you typed the question correctly.
Since the Richter scale is a logarithmic one, the answer to (b) is obviously "no".
A magnitude 4 earthquake causes very little damage, even near the epicenter. A magnitude 8 earthquake can destroy buildings, bridges, elevated highways, and dams. Seismograph amplitudes will be about 10,000 times higher. (Note that Log(base10) of 10^4 = 4)
a) To determine the magnitude of an earthquake with a seismographic reading of 1 mm, we can use the Richter scale equation: M(x) = log(x/x0).
Here, x is the seismographic reading of the earthquake (1 mm) and x0 is the seismographic reading of a zero-level earthquake (0.001 mm).
So, substituting the values in the equation:
M(1) = log(1/0.001)
To calculate this, we plug the expression in a calculator or use logarithmic properties to simplify it. The result will be the magnitude of the earthquake with a seismographic reading of 1 mm.
b) No, it is not true that an earthquake of magnitude 8 is twice as intense as an earthquake of magnitude 4. The Richter scale is logarithmic, which means that each increase in magnitude represents a tenfold increase in the amplitude of the seismic waves and approximately 31.6 times the energy release.
In this case, the earthquake of magnitude 8 would be 10^(8-4) = 10^4 = 10,000 times more intense and release much more energy than the earthquake of magnitude 4.
c) To express the equation M = log(x/x0) in exponential form, we can use the definition of logarithms. The logarithm is the exponent to which a base must be raised to obtain a certain number. In this case, the base is 10.
So, we can rewrite log(x/x0) = M in exponential form as:
10^M = x/x0
d) To determine the seismographic reading of an earthquake measuring 6.1 on the Richter scale, we can use the equation in exponential form from part (c):
10^M = x/x0
Substituting the magnitude of the earthquake (M = 6.1) into the equation, we have:
10^6.1 = x/0.001
To calculate this, we use a calculator or exponential properties to solve for x. The result will be the seismographic reading of the earthquake in mm.