624 words - 3 pages

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).

Don’t be scared off by logs. Think of them as a short-cut way of writing large numbers.

For example, let’s say the intensity of an earthquake is 100,000,000. Can you imagine if

the papers published that big number? What would people think? Most people cannot

handle well numbers with large amounts of zeros (unless those people work for the

government ;-). Instead of writing 100,000,000, let’s just write how many zeros there

are. In this case, there are 8 zeros. That’s exactly what log10 is asking. 10 to what power

equals 100,000,000? 10 ...view middle of the document...

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 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.

Paste this worksheet into your Word document. b) Which earthquake had the highest Richter number?

c) Is there a correlation between Intensity and number of deaths? That is, 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, 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. If you need help, remember to first

divide both sides by 10. Then perform the same operation that we performed above to

convert R = log(I) to 10R

= I.

b) Use 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.

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