Discussion
A seismograph records a wave amplitude 1000 times larger for earthquake X than for earthquake Y at the same distance. The difference in their magnitudes is
Answer: B
Correct answer: 3.0
Magnitude is the base ten logarithm of amplitude, so a difference in magnitude corresponds to a ratio of amplitudes: \[ \Delta M = \log_{10}\left(\frac{A_X}{A_Y}\right) = \log_{10}(1000) = 3.0. \] The condition that both are recorded at the same distance matters, because otherwise the distance correction would have to be applied before the amplitudes could be compared.
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