3.4 Logarithmic Functions

MAT 117
Logarithmic Functions 3.4
1. In 1935 Charles Richter defined the magnitude of an earthquake to be M  log 10
where I is
the intensity of the earthquake measured by the amplitude of a seismograph reading taken 100
km from the epicenter of the earthquake) and S is the intensity of a “standard earthquake”
(whose amplitude is 1micron= 10 cm). The San Francisco earthquake of 1906 has been
estimated to have registered around 8 on the Richter scale. In 2011, there was an earthquake in
the San Francisco bay area which registered 3.8 on the Richter scale. How many times more
intense was the 1906 earthquake than the 2011 earthquake?
2. Decibels provide a relative measure of sound intensity. The standard formula is
 I 
I dB   10 log 10   where I is the sound intensity and I 0 is the standard threshold of
 I0 
One reason powers of 10 are used for sound measurement is the rule of thumb for loudness: it
takes about 10 times the intensity to sound twice as loud. A loud rock concert can be measured
as high as 115 dB whereas normal conversation is around 65 dB. Determine how many times
more intense a loud rock concert is than normal conversation.
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