1. Logarithmic Scales: Earthquakes, Sounds, and Acids
Unit 8D
Logarithmic Scales: Earthquakes, Sounds, and Acids
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2. Distribution of Earthquakes
The map shows the distribution of earthquakes around the world. Each dot represents an earthquake.
SOURCE: U.S. Geological Survey
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3. The Magnitude Scale for Earthquakes
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:
log10E = M or E =(2.5 x 104) x 101.5M
The energy is measured in joules; magnitudes have no units.
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4. 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:
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5. Typical Sounds in Decibels
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6. The Inverse Square Law for Sound
The intensity of sound decreases with the square of the distance from the source, meaning that the intensity is proportional to 1/d2. 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.
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7. 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 = log10[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.
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8. Typical pH Values
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