Logs and Richter Scale, Decibels
Due: Wednesday, February 27th
Open the file found on the . You will use this file for both parts below. Click on the worksheet tabs at the bottom to access the decibel data.
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. An R of 2 means an intensity of 100 while an R of 3 has an intensity of 1000 which is 10 times larger than the previous intensity.
a) Open the ...view middle of the document...
It depends where the earthquake occurs. If it happens in a small town it will cause more deaths than if it has the same intensity and it happens in a larger city.
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?
100 times more intense.
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?
The number with the higher intensity has a larger Richter number.
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, and Io is the intensity of the softest sound that can be heard by humans.
I/Io is a ratio. This ratio is how many times louder a sound is 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. (See lecture notes)
b) Open the decibels worksheet. Using the formula above and the converted 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 one sound to be 10 decibels louder than another sound? If one sound is 10dB louder than another it just raises the other power exponentially.
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? 120dB=10^12 one plain
What would the ratio of intensities be for all three planes?
120dB=10^12 one plain
10^13=130db two plains
10^14=140db three plains
What would the decibel level be for the three jets? Is it 360 decibels as claimed above?
It would be 140 dB, 360 is not correct because everyone would be deaf.