Logarithmic Scales - Section 8D Mth 111 Mathematics as Human Pursuit Lab

Earthquakes The magnitude scale for earthquakes is defined so that each magnitude represents about 32 times as much energy as the prior magnitude. The formulas relating released energy (E) in joules to magnitude (M) are given by 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 or equivalently LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYmLUkjbWlHRiQ2I1EhRictRiM2Jy1GLDYlUSJFRicvJSdpdGFsaWNHUSV0cnVlRicvJSxtYXRodmFyaWFudEdRJ2l0YWxpY0YnLUkjbW9HRiQ2LVEiPUYnL0Y4USdub3JtYWxGJy8lJmZlbmNlR1EmZmFsc2VGJy8lKnNlcGFyYXRvckdGQi8lKXN0cmV0Y2h5R0ZCLyUqc3ltbWV0cmljR0ZCLyUobGFyZ2VvcEdGQi8lLm1vdmFibGVsaW1pdHNHRkIvJSdhY2NlbnRHRkIvJSdsc3BhY2VHUSwwLjI3Nzc3NzhlbUYnLyUncnNwYWNlR0ZRLUYjNigtSSNtbkdGJDYkUSQyLjVGJ0Y+LUY7Ni1RMSZJbnZpc2libGVUaW1lcztGJ0Y+RkBGQ0ZFRkdGSUZLRk0vRlBRJjAuMGVtRicvRlNGaG4tRiM2JC1JJW1zdXBHRiQ2JS1GVzYkUSMxMEYnRj4tRlc2JFEiNEYnRj4vJTFzdXBlcnNjcmlwdHNoaWZ0R1EiMEYnRj5GWi1GXW82JUZfby1GIzYmLUZXNiRRJDEuNUYnRj5GWi1GLDYlUSJNRidGNEY3Rj5GZW9GPkYrRj5GK0Y+. See the U.S. Geological Survey Earthquake Hazards Program Webster: http://earthquake.usgs.gov/ for lots of information about earthquakes. Example See Practice Test Question 26: a) On April 16th, 2008 there was an earquake nearVincinnes, IN of magnitude 5.1 How much energy in joules is released by an earthquake of magnitude 5.1? JSFH b) On Wed. Sept 2nd, 2009 there was a magnitude 7 earthquake in Indonesia. How much energy in joules is released by an earthquake of magnitude 5.1? JSFH From the computations above we can conclude that this magnitude 7 is almost ______ times as strong as the magnitude 5.1. JSFH JSFH

JSFH

Exercise: Go to the web site listed above and find the magnitudes of the May 12, 2008 earthquake in Eastern Sichuan, China Look up the magnitude of the largest earthquake recorded since 1900 in Chile, May 22, 1960. Compare as before their relative instensities. LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYjLUkjbWlHRiQ2I1EhRic= LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYjLUkjbWlHRiQ2I1EhRic=

Sound -- we use dB to denote loudness in number of decibels, and IR to denote the ratio of (intensity of the sound ) / (intensity of softest audible sound). The relationship between decibels and intensity are given by the formula loudness in decibels = LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYmLUkjbWlHRiQ2I1EhRictRiM2Ji1JI21uR0YkNiRRIzEwRicvJSxtYXRodmFyaWFudEdRJ25vcm1hbEYnLUkjbW9HRiQ2LVExJkludmlzaWJsZVRpbWVzO0YnRjUvJSZmZW5jZUdRJmZhbHNlRicvJSpzZXBhcmF0b3JHRj4vJSlzdHJldGNoeUdGPi8lKnN5bW1ldHJpY0dGPi8lKGxhcmdlb3BHRj4vJS5tb3ZhYmxlbGltaXRzR0Y+LyUnYWNjZW50R0Y+LyUnbHNwYWNlR1EmMC4wZW1GJy8lJ3JzcGFjZUdGTS1JJW1zdWJHRiQ2JS1GLDYlUSRsb2dGJy8lJ2l0YWxpY0dGPkY1LUYjNiRGMUY1LyUvc3Vic2NyaXB0c2hpZnRHUSIwRidGNUYrRjU=(Intensity ratio of sound to softest audible sound) or using our abbreviations: 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 Alternatively we have an equivalent formula: 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 For example: If we have a sound that has an intensity ratio IR of 100 (Example 3 page 549), we would use the first form to compute its loudness in decibels. LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYjLUkjbWlHRiQ2I1EhRic= On the other hand if we are given a loudness in decibels of 20, we use the second form to compute its intensity ratio: LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYjLUkjbWlHRiQ2I1EhRic= Practice Test Question 17: A sound of what loudness in decibels is 63 times as intense as a 13 dB sound? Step 1: Compute the intensity ratio of the 13 dB sound. JSFH Step 2: Compute an intensity ratio 63 times you intensity ratio computed in Step 1. LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYlLUkjbW5HRiQ2JFEjNjNGJy8lLG1hdGh2YXJpYW50R1Enbm9ybWFsRictSSNtb0dGJDYtUScmc2RvdDtGJ0YvLyUmZmVuY2VHUSZmYWxzZUYnLyUqc2VwYXJhdG9yR0Y4LyUpc3RyZXRjaHlHRjgvJSpzeW1tZXRyaWNHRjgvJShsYXJnZW9wR0Y4LyUubW92YWJsZWxpbWl0c0dGOC8lJ2FjY2VudEdGOC8lJ2xzcGFjZUdRJjAuMGVtRicvJSdyc3BhY2VHRkctRiw2JFEsMTkuOTUyNjIzMTVGJ0Yv

JCIrZV8sZDchIic=

Step 3: Compute the corresponding decibels for this intensity ratio. LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYnLUkjbWlHRiQ2I1EhRictSSNtbkdGJDYkUSMxMEYnLyUsbWF0aHZhcmlhbnRHUSdub3JtYWxGJy1JI21vR0YkNi1RJyZzZG90O0YnRjMvJSZmZW5jZUdRJmZhbHNlRicvJSpzZXBhcmF0b3JHRjwvJSlzdHJldGNoeUdGPC8lKnN5bW1ldHJpY0dGPC8lKGxhcmdlb3BHRjwvJS5tb3ZhYmxlbGltaXRzR0Y8LyUnYWNjZW50R0Y8LyUnbHNwYWNlR1EmMC4wZW1GJy8lJ3JzcGFjZUdGSy1GLDYlUSZsb2cxMEYnLyUnaXRhbGljR0Y8RjMtSShtZmVuY2VkR0YkNiQtRiM2Iy1GMDYkUSwxMjU3LjAxNTI1OEYnRjNGMw==

JCIrXDBNKjQkISIp

Try Exercise 29 page 554: (Compute the IR of each sound and then take their ratio.) LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYjLUkjbWlHRiQ2I1EhRic= LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYjLUkjbWlHRiQ2I1EhRic= LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYjLUkjbWlHRiQ2I1EhRic= LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYjLUkjbWlHRiQ2I1EhRic= Inverse Square Law for Sound: Intensity of sound is inversely proportional to the square of the distance from the source of the sound. This gives the Inverse Square Law: 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 (Here K is a constant) For example if you move from 5 feet from a band performing to 15 feet away, you have moved 3 times further away and reduced the intensity by a factor 32 = 9. The sound is 9 times less intense. If you moved to 50 feet away, you have moved 10 times further away. Thus the sound intensity has decreased by a factor of 102 = 100 times less intense. (Example 5, page 550) At 30 meters the sound of a jet has an intensity of a 140 decibel sound. How far away do we need to be to receive a 120 decibel sound? (First we compute the ratio of the intensity of the 30 meters away jet sound (140 decibels) to a 120 decibel jet sound) JSFH Since the 120 decibel sound is 100 times less intense than the 140 decibel sound, moving 10 times further away to 300 meters, will give us a 1LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYnLUkjbWlHRiQ2I1EhRictRiM2J0YrLUYjNiQtSSVtc3VwR0YkNiUtSSNtbkdGJDYkUSIwRicvJSxtYXRodmFyaWFudEdRJ25vcm1hbEYnLUY3NiRRIjJGJ0Y6LyUxc3VwZXJzY3JpcHRzaGlmdEdRIjBGJ0Y6RisvJStiYWNrZ3JvdW5kR1EuWzI1NSwyNTUsMjU1XUYnRjpGK0ZDRjo= = 100 times less intense sound. We confirm this by making Maple solve the appropriate equation: 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 We of course are interested in the positive solution only.

Finding pH. The pH Scale is defined by [H+ ] = 10-pH. where H is the hydrogen ion concentration in moles per liter. Equivalently pH = -log 10[H+] 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 LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYlLUkjbWlHRiQ2I1EhRictRiM2JS1GLDYlUSNwSEYnLyUnaXRhbGljR1EldHJ1ZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJy1JI21vR0YkNi1RKiZjb2xvbmVxO0YnL0Y4USdub3JtYWxGJy8lJmZlbmNlR1EmZmFsc2VGJy8lKnNlcGFyYXRvckdGQi8lKXN0cmV0Y2h5R0ZCLyUqc3ltbWV0cmljR0ZCLyUobGFyZ2VvcEdGQi8lLm1vdmFibGVsaW1pdHNHRkIvJSdhY2NlbnRHRkIvJSdsc3BhY2VHUSwwLjI3Nzc3NzhlbUYnLyUncnNwYWNlR0ZRLUkjbW5HRiQ2JFEkNy4wRidGPkYr 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 Practice Test 19. How much more acidic (in terms of ratios) is acid rain with a pH of 3.5 than ordinary rain with a pH of 6? Step 1: Compute Hydrogen Ion concentration for a pH of 6.0: JSFH Step 2: Compute Hydrogen Ion concentration for a pH of 3.5: JSFH Step 3: Take the ratio of your answers: JSFH Or Short Cut Method: Just take 10 raised to the amount by which the pH decreases: JSFH