ISP 120 - Quantitative Reasoning
Group Activity 15: Logs and Richter Scale, Decibels, and pH scale

 

All group activities must include a statement signed by all members of your group that each group member fully participated in the activity. To start you should open a new Word document entitled something like "Group Activity 15" and put the names of your group members at the top. Save it to the desktop.

 

Open the file logs.xls.  You will use this file for all three parts below.  Click on the worksheet tabs at the bottom to access the other files.

 

1. Richter scale

The Richter scale is used to measure the intensity of earthquakes.  It is a logarithmic relationship with the following formula:

 

R = log I

 

I is the intensity of the earthquake and R is the number on the Richter scale. 

(Remember that if there is no base written with the log it is base 10).  Converting the above formula from log form to exponent form would give us:

10R = I

 

Which version you use depends on which variable you are given. 

 

Since the Richter scale is logarithmic, an increase of 1 on the Richter scale translates to 10 times increase in intensity.  Ie. R of 2 means an intensity of 100 while an R or 3 has an intensity of 1000 which is 10 times larger than the previous intensity.

 

a) Open the Richter worksheet in the Excel file.  For the first 9 earthquakes, calculate the Richter number and for the remaining calculate the intensity using the formulas above. 

 

b) Which earthquake had the highest Richter number?

 

c) Is there a correlation between Intensity and number of deaths?  Meaning as the intensity of the earthquakes increased, did the number of deaths increase?  Why do you think that is?

 

d) If one earthquake had a Richter number of 5 and another had a Richter number of 7, how many times more intense would the second one be than the first?

 

e) If one earthquake had an intensity of 8,000,000 and another had an intensity of 80,000,000 how, specifically, would their Richter numbers compare?

 

 

 

2. Decibels

 

Decibels are a measurement of sound intensity.  The logarithmic relationship between intensity of a sound and sound level in decibels is given by the following formula:

 

L = 10 * log ( I/Io)

 

L is the sound level in decibels I is the intensity of the sound Io is the intensity of the softest sound that can be heard by humans (10-12)

I/Io is the ratio.  This ratio is how many times louder than the softest audible sound. For this activity, we will only consider the ratio and not the individual pieces of the ratio.

 

a) Convert the above formula to exponent form.

 

 

b) Open the decibels worksheet.  Using the formula above and the version from part a), fill in the empty cells with either the decibels or the ratios of the intensities.  Copy and paste the table into your Word document. 

 

 

c) What does it mean mathematically about the ratio of intensity for a one sound to be 10 decibels louder than another sound?

 

 

d) The following statement is incorrect.

“A jet airplane landing at the local airport makes 120 decibels of noise.  If we allow three jets to land at the same time, there will be 360 decibels of noise pollution.”

 

If one jet airplane makes 120 decibels of noise, what would the ratio of intensities be for one plane?

What would the ratio of intensities be all three planes?

What would the decibel level be for the three jets?  Is it 360 decibels as claimed above?

 

 

 

 

3. pH scale

 

The pH scale describes the relative acidity or basicity of a substance.  To the chemist, pH is a measure of the concentration of positive hydrogen ions, H+, in a solution.  The pH scale generally ranges from 1 to 14.  Pure distilled water at 25C (about room temperature) is said to be neutral and has a pH of 7.  Solutions with pH less than 7 are acidic and solutions with pH greater than 7 are basic.   The relationship between pH and the hydrogen ion concentration is a logarithmic function with the following formula:

 

pH = -log [H+]

 

where [H+]  is the symbol for hydrogen ion concentration. 

 

a)  Convert the above formula to exponent form. 

 

b) Borax, a cleaning agent, has a pH of 9.2.  Is it basic or acidic?  What is the H+ concentration? 

 

c) Open the pH worksheet.  Fill in the empty cells using the formula above with either the pH or the hydrogen ion concentration.  Copy and paste the completed table into your Word document. 

 

d) What does it mean mathematically about the Hydrogen ion concentration for a one substance to have a pH of 1 more than another?