1. One way to define the magnitude M of an earthquake is to use the Richter scale, which is given by the formula
where the intensity of the earthquake is T times greater than the intensity of the smallest earthquake that can be measured.
The Nisqually earthquake on February 28, 2001 was one of the largest recorded earthquakes in Washington state history. The quake measured 6.8 on the Richter scale. The Mar 11, 2011 earthquake in Japan was measured as a 9.0 magnitude earthquake. It was the most powerful known earthquake to have hit Japan, and it is one of the five most powerful earthquakes in the world since record-keeping began in 1900.
The intensity of the Japanese earthquake was how many times greater than the intensity of the Nisqually earthquake?
2. If the magnitude of an earthquake is known, then the energy E released, measured in joules, during the earthquake is given by,
where joules.
During the Japanese earthquake on Mar 11, 2011, which had a magnitude of 9.0, how much energy was released?
3. When the loudness of a sound is to be determined, the intensity I of the sound is compared to the minimum intensity of sound that a person can hear by the formula
where Io is the minimum (or threshold) level of sound that can be heard by human beings (Io = 10-12 W/m2).
a) For normal conversation, the sound level is measured to be about 60 decibels. What is the sound intensity of a normal conversation?
b) The intensity of sound measured from a barking dog is W/m2. What is the
decibel level of this sound?
Optional part which would be appropriate for Math 141 to see where the sound intensity came from:
Assume that the lowest elevation that the Blue Angels fly over a crowd is 1500 feet (457 m). At a constant throttle setting, the acoustic power emitted from a jet engine will be constant. A jet engine has a sound intensity of about 103 W/m2 at a distance of 10 m. The relationship between sound intensity and power is
We know one distance and the engine’s sound intensity at that distance
We also know one other distance where we want to find the sound intensity.
Solve both equations for P since the power put out from a jet engine is the same at both distances.
And set them equal to each other.
Solve for I.
This gives the sound intensity on the ground.
I 4.9 x 10-2 W/m2
4. In chemistry, the pH of a solution is the measure of the acidity of the solution. The definition for pH is
pH = -log[H+]
where [H+] is the concentration of the hydrogen ion in moles per liter. The range for pH is from 0 to 14.
All plants have a range of pH values over which they grow best. Assume you have a patch of land where you want to grow a small herb garden. When you measure the soil, you find that the hydrogen ion concentration is 1.3 x 10-6 moles per liter.
a) Find the pH of the soil in the garden.
b) From the following list of plants, which ones would survive the best if you don’t want to change the pH of the soil?
Herb Ideal pH
Basil 5.5 – 6.5
Chives 6.0 – 7.0
Garlic 5.5 – 7.5
Ginger 6.0 – 8.0
Mint 7.0 – 8.0
Parsley 5.0 – 7.0
Sage 5.5 – 6.5
Thyme 5.5 – 7.0
.
5. Salmonella is a bacteria that can make humans sick if they eat food contaminated with the bacteria. One common source of salmonella is in eggs that are not properly cooked. With summer approaching, food left out during warm weather can provide a fertile growing environment if there is initially some salmonella in the food.
The time in hours that it takes for an initial population P0 of salmonella to increase in size to P is given by the formula
a) Rewrite this formula in a simplified form using the properties of logarithms.
Answers
1.
Japanese earthquake: Nisqually earthquake:
The Japanese earthquake was about 160 times more powerful than the Nisqually earthquake.
2.
Joules of energy
By comparison, the atomic bomb dropped on Hiroshima during World War II released 63 x 1012 joules of energy.
3. a)
W/m2
b) decibels
c)
5a)
b)
