Logarithmic scale - Revision history

Jmdonev: 1 revision imported

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energy>Jmdonev at 19:00, 7 January 2021

2021-01-07T19:00:29Z

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	[[Category:~~Done_2015~~-09-06]]		[[Category:Done 2021-01-31]]
	[[File:LogLinScale.png\|400px\|thumb\|Figure 1. A semi log plot with three different functions graphed (click to enlarge).<ref>Wikimedia Commons [Online], Available: https://upload.wikimedia.org/wikipedia/commons/4/46/LogLinScale.svg</ref>]]		[[File:LogLinScale.png\|400px\|thumb\|Figure 1. A semi log plot with three different functions graphed (click to enlarge).<ref>Wikimedia Commons [Online], Available: https://upload.wikimedia.org/wikipedia/commons/4/46/LogLinScale.svg</ref>]]

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	==References==		==References==
	{{reflist}}[[Category:Uploaded]]		{{reflist}}
			[[Category:Uploaded]]

Jmdonev at 05:54, 26 October 2017

2017-10-26T05:54:17Z

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	<center><math>dB=10 \times log_{10}(\frac{I}{I_o})</math></center>		<center><math>dB=10 \times log_{10}(\frac{I}{I_o})</math></center>

	:where <m>I_o</math> is the threshold of hearing and <m>I</math> is the intensity of the sound.<ref name=hyp>Hyperphysics. (August 25, 2015). ''Decibels'' [Online], Available: http://hyperphysics.phy-astr.gsu.edu/hbase/sound/db.html</ref> A conversation is roughly 1 million times more intense than the threshold value. The corresponding decibel value is then		:where <math>I_o</math> is the threshold of hearing and <math>I</math> is the intensity of the sound.<ref name=hyp>Hyperphysics. (August 25, 2015). ''Decibels'' [Online], Available: http://hyperphysics.phy-astr.gsu.edu/hbase/sound/db.html</ref> A conversation is roughly 1 million times more intense than the threshold value. The corresponding decibel value is then

	<center><math>dB=10 \times log_{10}(\frac{10^6I_o}{I_o})=10 \times log_{10}(10^6)=10 \times 6 = 60 dB</math></center>		<center><math>dB=10 \times log_{10}(\frac{10^6I_o}{I_o})=10 \times log_{10}(10^6)=10 \times 6 = 60 dB</math></center>

Jmdonev at 05:53, 26 October 2017

2017-10-26T05:53:47Z

← Older revision		Revision as of 05:53, 26 October 2017
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	*'''The pH scale''' - A commonly used logarithmic scale is [[the pH scale]], used when analyzing [[acid]]s and [[base (chemistry)\|bases]]. What the pH scale is doing is measuring the concentration of [[hydrogen]] [[ion]]s (H<sup>+</sup>) in a substance, and is given by the equation		*'''The pH scale''' - A commonly used logarithmic scale is [[the pH scale]], used when analyzing [[acid]]s and [[base (chemistry)\|bases]]. What the pH scale is doing is measuring the concentration of [[hydrogen]] [[ion]]s (H<sup>+</sup>) in a substance, and is given by the equation

	<center><m>10^{-pH}=H^+</m></center>		<center><math>10^{-pH}=H^+</math></center>

	:By this, for every ''one'' decrease (due to the negative sign) in the pH, the acidity increases by a factor of ''ten'' (A pH of 3 is 10 times more acidic than a pH of 4, and is 100 times more acidic than a pH of 5).		:By this, for every ''one'' decrease (due to the negative sign) in the pH, the acidity increases by a factor of ''ten'' (A pH of 3 is 10 times more acidic than a pH of 4, and is 100 times more acidic than a pH of 5).
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	*'''Sound''' - The way [[sound]] is picked up by one's ears is of logarithmic nature. The '''decibel''' (dB) system of sound intensity is a measure of how loud a sound is to one's ears. It is represented by the equation		*'''Sound''' - The way [[sound]] is picked up by one's ears is of logarithmic nature. The '''decibel''' (dB) system of sound intensity is a measure of how loud a sound is to one's ears. It is represented by the equation

	<center><m>dB=10 \times log_{10}(\frac{I}{I_o})</m></center>		<center><math>dB=10 \times log_{10}(\frac{I}{I_o})</math></center>

	:where <m>I_o</m> is the threshold of hearing and <m>I</m> is the intensity of the sound.<ref name=hyp>Hyperphysics. (August 25, 2015). ''Decibels'' [Online], Available: http://hyperphysics.phy-astr.gsu.edu/hbase/sound/db.html</ref> A conversation is roughly 1 million times more intense than the threshold value. The corresponding decibel value is then		:where <m>I_o</math> is the threshold of hearing and <m>I</math> is the intensity of the sound.<ref name=hyp>Hyperphysics. (August 25, 2015). ''Decibels'' [Online], Available: http://hyperphysics.phy-astr.gsu.edu/hbase/sound/db.html</ref> A conversation is roughly 1 million times more intense than the threshold value. The corresponding decibel value is then

	<center><m>dB=10 \times log_{10}(\frac{10^6I_o}{I_o})=10 \times log_{10}(10^6)=10 \times 6 = 60 dB</m></center>		<center><math>dB=10 \times log_{10}(\frac{10^6I_o}{I_o})=10 \times log_{10}(10^6)=10 \times 6 = 60 dB</math></center>

	:Now, if two people are talking at once, that only raises the dB to 63 dB. So a ''doubling'' of sound intensity just leads to ''+3dB''. The threshold of pain is about 120 dB and that causes hearing loss.		:Now, if two people are talking at once, that only raises the dB to 63 dB. So a ''doubling'' of sound intensity just leads to ''+3dB''. The threshold of pain is about 120 dB and that causes hearing loss.

Jmdonev at 05:52, 26 October 2017

2017-10-26T05:52:24Z

← Older revision		Revision as of 05:52, 26 October 2017
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	A basic equation for a base ten logarithmic plot is		A basic equation for a base ten logarithmic plot is

	<center><m>y=log_{10}(x)</m></center>		<center><math>y=log_{10}(x)</math></center>

	which can be rearranged to		which can be rearranged to

	<center><m>10^y=x</m></center>		<center><math>10^y=x</math></center>

	What this means is that for every ''one'' value of y, the value of x will increase by a factor of ''ten'', and vice versa. Using a logarithmic scale can be useful when creating graphs to compress the scale and make the data easier to comprehend. When plotted on a semi-log plot, seen in Figure 1, the exponential 10<sup>x</sup> function appears linear, when it would normally diverge quickly on a linear graph.		What this means is that for every ''one'' value of y, the value of x will increase by a factor of ''ten'', and vice versa. Using a logarithmic scale can be useful when creating graphs to compress the scale and make the data easier to comprehend. When plotted on a semi-log plot, seen in Figure 1, the exponential 10<sup>x</sup> function appears linear, when it would normally diverge quickly on a linear graph.
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	:By this, for every ''one'' decrease (due to the negative sign) in the pH, the acidity increases by a factor of ''ten'' (A pH of 3 is 10 times more acidic than a pH of 4, and is 100 times more acidic than a pH of 5).		:By this, for every ''one'' decrease (due to the negative sign) in the pH, the acidity increases by a factor of ''ten'' (A pH of 3 is 10 times more acidic than a pH of 4, and is 100 times more acidic than a pH of 5).

	[[File:pHacid.png\|800px\|thumb\|center\|Figure 2. The pH scale, along with examples of substances and their acidity.<ref>''Created internally by a ~~memer~~ of the Energy Education team'': Adapted from Energy: Its use and the Environment.</ref>]]		[[File:pHacid.png\|800px\|thumb\|center\|Figure 2. The pH scale, along with examples of substances and their acidity.<ref>''Created internally by a member of the Energy Education team'': Adapted from Energy: Its use and the Environment.</ref>]]

J.williams: 1 revision imported

2015-09-18T16:51:03Z

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J.williams at 21:50, 3 September 2015

2015-09-03T21:50:53Z

← Older revision		Revision as of 21:50, 3 September 2015
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	[[Category:Done_2015-09-05]]		[[Category:Done_2015-09-06]]
	[[File:LogLinScale.png\|400px\|thumb\|Figure 1. A semi log plot with three different functions graphed (click to enlarge).<ref>Wikimedia Commons [Online], Available: https://upload.wikimedia.org/wikipedia/commons/4/46/LogLinScale.svg</ref>]]		[[File:LogLinScale.png\|400px\|thumb\|Figure 1. A semi log plot with three different functions graphed (click to enlarge).<ref>Wikimedia Commons [Online], Available: https://upload.wikimedia.org/wikipedia/commons/4/46/LogLinScale.svg</ref>]]

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	*'''Sound''' - The way sound is picked up by one's ears is of logarithmic nature. The '''decibel''' (dB) system of sound intensity is a measure of how loud a sound is to one's ears. It is represented by the equation		*'''Sound''' - The way [[sound]] is picked up by one's ears is of logarithmic nature. The '''decibel''' (dB) system of sound intensity is a measure of how loud a sound is to one's ears. It is represented by the equation

	<center><m>dB=10 \times log_{10}(\frac{I}{I_o})</m></center>		<center><m>dB=10 \times log_{10}(\frac{I}{I_o})</m></center>
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	==References==		==References==
	{{reflist}}		{{reflist}}[[Category:Uploaded]]

J.williams: 1 revision imported

2015-09-03T18:21:53Z

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Jmdonev at 18:04, 26 August 2015

2015-08-26T18:04:49Z

New page

[[Category:Done_2015-09-05]]
[[File:LogLinScale.png|400px|thumb|Figure 1. A semi log plot with three different functions graphed (click to enlarge).<ref>Wikimedia Commons [Online], Available: https://upload.wikimedia.org/wikipedia/commons/4/46/LogLinScale.svg</ref>]]

<onlyinclude>A '''logarithmic scale''' is a nonlinear scale often used when analyzing a large range of quantities. Instead of increasing in equal increments, each interval is increased by a '''factor of the base of the logarithm'''. Typically, a '''base ten''' and '''base ''e''''' scale are used.</onlyinclude>

A basic equation for a base ten logarithmic plot is

<center><m>y=log_{10}(x)</m></center>

which can be rearranged to

<center><m>10^y=x</m></center>

What this means is that for every ''one'' value of y, the value of x will increase by a factor of ''ten'', and vice versa. Using a logarithmic scale can be useful when creating graphs to compress the scale and make the data easier to comprehend. When plotted on a semi-log plot, seen in Figure 1, the exponential 10<sup>x</sup> function appears linear, when it would normally diverge quickly on a linear graph.

This is useful for many applications, some of which will be seen below.

===Examples===

*'''The pH scale''' - A commonly used logarithmic scale is [[the pH scale]], used when analyzing [[acid]]s and [[base (chemistry)|bases]]. What the pH scale is doing is measuring the concentration of [[hydrogen]] [[ion]]s (H<sup>+</sup>) in a substance, and is given by the equation

<center><m>10^{-pH}=H^+</m></center>

:By this, for every ''one'' decrease (due to the negative sign) in the pH, the acidity increases by a factor of ''ten'' (A pH of 3 is 10 times more acidic than a pH of 4, and is 100 times more acidic than a pH of 5).

[[File:pHacid.png|800px|thumb|center|Figure 2. The pH scale, along with examples of substances and their acidity.<ref>''Created internally by a memer of the Energy Education team'': Adapted from Energy: Its use and the Environment.</ref>]]

*'''Sound''' - The way sound is picked up by one's ears is of logarithmic nature. The '''decibel''' (dB) system of sound intensity is a measure of how loud a sound is to one's ears. It is represented by the equation

<center><m>dB=10 \times log_{10}(\frac{I}{I_o})</m></center>

:where <m>I_o</m> is the threshold of hearing and <m>I</m> is the intensity of the sound.<ref name=hyp>Hyperphysics. (August 25, 2015). ''Decibels'' [Online], Available: http://hyperphysics.phy-astr.gsu.edu/hbase/sound/db.html</ref> A conversation is roughly 1 million times more intense than the threshold value. The corresponding decibel value is then

<center><m>dB=10 \times log_{10}(\frac{10^6I_o}{I_o})=10 \times log_{10}(10^6)=10 \times 6 = 60 dB</m></center>

:Now, if two people are talking at once, that only raises the dB to 63 dB. So a ''doubling'' of sound intensity just leads to ''+3dB''. The threshold of pain is about 120 dB and that causes hearing loss.

<center>'''Visit [http://hyperphysics.phy-astr.gsu.edu/hbase/sound/db.html Hyperphysics] for more details.</center>

*'''The Richter Scale''' - Earthquakes are measured on the Richter Scale, which is a base 10 logarithmic scale. This scale measures the magnitude of an earthquake, which is the amount of [[energy]] released by it. For every single increase on this scale, the magnitude is increased by a factor of 10.<ref>Harris, Tom, and Patrick J. Kiger. (August 24, 2015). "How Earthquakes Work". HowStuffWorks.com [Online], Available: http://science.howstuffworks.com/nature/natural-disasters/earthquake.htm</ref> Visit [http://science.howstuffworks.com/nature/natural-disasters/earthquake.htm HowStuffWorks] to learn more.

==References==
{{reflist}}