1. Section 8D Logarithmic Scales: Earthquakes, Sounds, & Acids
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2. Logarithmic Scales Earthquake strength is described in magnitude.
Loudness of sounds is described in decibels.
Acidity of solutions is described by pH.
Each of these measurement scales involves exponential growth.
Successive numbers on the scale increase by the same relative amount.
e.g. A liquid with pH 5 is ten times more acidic than one with pH 6.

3. Earthquakes – Relative Energy
8-D
Earthquakes – Relative Energy

4. Approximate number per year (Worldwide average since 1900)
Magnitude Scale
Category
Magnitude
Approximate number per year
(Worldwide average since 1900)
Great
8 and up 1
Major
7-8 18
Strong
6-7
120
Moderate
5-6
800
Light
4-5
6000
Minor
3-4
50,000
Very minor
Less than 3
1,000 / 8,000 per day

5. Earthquakes – Relative Energy
8-D
Earthquakes – Relative Energy

6. The Earthquake Magnitude Scale
The scale is designed so that each magnitude (M) represents about 32 times as much energy as the prior magnitude.

7. Examples: Sumatra: Dec. 26, 2004 magnitude = 9 283,106 deaths
Mexico earthquake: Sept. 19, 1985
magnitude = 8 9,500 deaths
Since each magnitude increase (of 1) means approximately 32 times as much energy-
The December Sumatra released about 32 times as much energy as the 1985 Mexico earthquake, and resulted in almost 30 times as many deaths.
32*9500 = 304, so in this case there is a relatively close match between magnitude/energy and number of deaths.

9. The Earthquake Magnitude Scale
Where is the ‘almost 32 times as much energy’ coming from?
Ah ha!

10. New Guinea earthquake (June 25, 1976):
8-D
New Guinea earthquake (June 25, 1976):
magnitude = energy = ×1015 joules
# deaths = 422
Afghanistan earthquake (May 30, 1998):
magnitude = 6.9 energy = ×1014 joules
# deaths = 4000
Energy New Guinea = ×1015 = 1.995
Energy Afghanistan ×1014
New Guinea earthquake was about twice as strong as the Afghanistan earthquake.

11. Another way: New Guinea earthquake: 7.1 magnitude
Afghanistan earthquake: magnitude
Difference in magnitude = = .2

13. 8-D
Measuring Sound
The decibel scale is used to compare the loudness of sounds.
Designed so that 0 dB represents the softest sound audible to the human ear.

14. Typical Sounds in Decibels
Times Louder than Softest Audible Sound
Example
140
1014
jet at 30 meters
120
1012
strong risk of damage to ear
100
1010
siren at 30 meters 90
109
threshold of pain for ear 80
108
busy street traffic 60
106
ordinary conversation 40
104
background noise 20
102
whisper 10
rustle of leaves 1
threshold of human hearing
-10
0.1
inaudible sound
Table 8.5 from text
decibels increase by 10 and intensity is multiplied by 10.

15. 8-D
Measuring Sound
The loudness of a sound in decibels is defined by the following equivalent formulas:

16. 8-D
Example
What is the loudness, in dB, of a sound 25 million times as loud as the softest audible sound?

17. 8-D
Example
What is the loudness, in dB, of a sound 25 million times as loud as the softest audible sound?

18. 8-D
Example
How much more intense is a 47-dB sound than a 13-dB sound?

20. pH Scale The pH scale is defined by the following equivalent formulas:
pH = log10[H+] or [H+] = 10pH
where [H+] is the hydrogen ion concentration in moles per liter.

21. Hydrogen concentration:
A mole
is Avogadro’s number of particles
= 6×1023 particles
So [H+] is measured in number of 6×1023 particles per liter

22. pH Scale The pH scale is defined by the following equivalent formulas:
pH = log10[H+] or [H+] = 10pH
Pure water is neutral and has a pH of 7.
[H+] = 107 = moles/liter
Acids have a pH lower than 7
Bases (alkaline solutions) have a pH higher than 7.

24. Typical pH values Solution pH Pure water 7 Drinking water 6.5-8
Stomach acid
2-3
Baking soda
8.4
Vinegar 3
Household ammonia 10
Lemon juice 2
Drain opener
10-12

25. Example
8-D
If the pH of a solution increases from 4 to 6, how much does the hydrogen ion concentration change? Does the change make the solution more acidic or more basic?
Initial concentration = [H1+] = 10-pH
= 10-4 =.0001 moles/liter
New concentration = [H2+] = 10-pH
= 10-6 = moles/liter
So it decreases
by a factor of = 10-4 = 100

26. Example
8-D
If the pH of a solution increases from 4 to 6, how much does the hydrogen ion concentration change? Does the change make the solution more acidic or more basic?
Pure water is neutral and has a pH of 7.
Acids have a pH lower than 7
Bases have a pH higher than 7.
This makes the solution more basic (less acidic).

27. Example
8-D
How much more acidic is acid rain with a pH of 3 than ordinary rain with a pH of 6?
We really want to know – how many times larger is the hydrogen concentration of the acid rain than that of ordinary rain?
Which means we need to look at the ratio of their hydrogen concentrations:

29. Example
8-D
How much more acidic is acid rain with a pH of 3 than ordinary rain with a pH of 6?
Ordinary rain: [H+] = 10-pH = mole per liter
Acid rain: [H+] = 10-pH = mole per liter
Ratio: = 1000
10-6
That is, this acid rain is 1000 times more acidic than ordinary rain.
Normal raindrops are mildly acidic, with a pH slightly under 6. However, the burning of fossil fuels releases sulfur or nitrogen that can form sulfuric or nitric acids in the air which can make raindrops far more acidic than normal. Acid rain in the NE U.S. and acid fog in LA have been observed with a pH as low as 2 – the same acidity as pure lemon juice!

31. 8-D
Homework:
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# 10, 12, 16, 19, 20, 26, 28, 34