Copyright © 2011 Pearson Education, Inc. Exponential Astonishment.

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Copyright © 2011 Pearson Education, Inc. Exponential Astonishment

Copyright © 2011 Pearson Education, Inc. Slide 8-3 Unit 8D Logarithmic Scales: Earthquakes, Sounds, and Acids

8-D Copyright © 2011 Pearson Education, Inc. Slide 8-4 SOURCE: U.S. Geological Survey The map shows the distribution of earthquakes around the world. Each dot represents an earthquake. Distribution of Earthquakes

8-D Copyright © 2011 Pearson Education, Inc. Slide 8-5 The magnitude scale for earthquakes is defined so that each magnitude represents about 32 times as much energy as the prior magnitude. The magnitude, M, is related to the released energy, E, by the following equivalent formulas: log 10 E = M or E =(2.5 x 10 4 ) x M The energy is measured in joules; magnitudes have no units. The Magnitude Scale for Earthquakes

8-D Copyright © 2011 Pearson Education, Inc. Slide 8-6 Measuring Sound The decibel scale is used to compare the loudness of sounds. The loudness of a sound in decibels is defined by the following equivalent formulas:

8-D Copyright © 2011 Pearson Education, Inc. Slide 8-7 Typical Sounds in Decibels

8-D Copyright © 2011 Pearson Education, Inc. Slide 8-8 The intensity of sound decreases with the square of the distance from the source, meaning that the intensity is proportional to 1/d 2. Therefore, sound follows and inverse square law with distance. How many times greater is the intensity of sound from a concert speaker at a distance of 10 meters than the intensity at a distance of 80 meters? The sound intensity at 10 meters is 64 times the sound intensity at 80 meters. The Inverse Square Law for Sound

8-D Copyright © 2011 Pearson Education, Inc. Slide 8-9 pH Scale The pH scale is used to classify substances as neutral, acidic, or basic. The pH scale is defined by the equivalent formula pH =  log 10 [H + ] or [H + ] = 10  pH where [H + ] is the hydrogen ion concentration in moles per liter. Pure water is neutral and has a pH of 7. Acids have a pH lower than 7 and bases have a pH higher than 7.

8-D Copyright © 2011 Pearson Education, Inc. Slide 8-10 Typical pH Values