SBM 8D Exponential Astonishment

1
SBM 8D Exponential Astonishment

• Logarithmic Scales
• Earthquakes, Sounds and Acids

2
.EARTHQUAKE.

• You have probably heard of the magnitude of an
  earthquake.
• Or the decibels of a home stereo.
• Or the pH of your hot tub or pool.
• All three of these are measured with an
  exponential scale.
• These logarithmic scales we have studied earlier
  in this chapter.

3
The Magnitude Scale...

• The magnitude scale for earthquakes is defined so
  that each magnitude represents about 32 times as
  much energy as the prior magnitude.
• More technically, the magnitude, M, is related to
  the released energy, E, by the following
  equivalent formulas on the next slide
• The energy is measured in Joules (see Unit
  2B) (Table 8.4)
• magnitudes have no units.

4
Magnitude Formulas(for Earthquakes)

• log10E 4.4 1.5 M
• E (2.5 x 104) x 101.5M

Please Look at Examples 1-2 on page 491
5
Measuring Sounds in Decibels...

• The decibel scale is used to compare the loudness
  of sounds.
• Zero decibels (or 0 dB) represents the softest
  audible sound to the human ear.
• Look at (Table 8.5) for approximate decibel
  levels of certain sounds.
• See the next slide for the Decibel-Formula(s)

6
The Decibel Scale for Sound

• The loudness of a sound in decibels is defined by
  the following equivalent formulas

Loudness in dB 10 log10
)
(
Intensity of the sound
Intensity of softest audible sound
Or see next Slide
7
The Decibel Scale for Sound

• The loudness of a sound in decibels is defined by
  the following equivalent formulas

)
(
Intensity of the sound

Intensity of softest audible sound
Loudness in dB

10
10
Please Look at Examples 3-4 on pages 492-93
8
The pH Scale for Acidity...

• If you check many household products, you will
  see they state a quantity called the pH.
• pH is classified as either
• Neutral
• Acidic
• Basic (or alkaline)

See Table 8.6 for Typical pH Values
9
The pH Scale...

• The pH scale is defined by the following
  equivalent formulas
• 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
• Bases have a pH higher than 7.

pH -log10 H H 10-pH
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More on pH...

• The concentration of positively charged hydrogen
  ions is acidity.
• To be a positively charged ion, atoms are without
  their electron.
• This measurement is moles per liter.
• A mole is a avogadros number of particles.
• This number is equivalent to about 6 x 1023
  particles.

Please Look at Example 6 on pages 494
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Homework...

• 8D s 1, 2, 7 - 9, 13 - 15, 19 - 21, 25
• Chapter 8 Test in 2 Blocks Start Studying!!
• See Chapter 8 Summary on page 497 - 498.