Logarithmic Scales 1

Instruction Richter Scale Definition: The Richter scale, which measures the magnitude of earthquakes, was developed in 1935 by Charles F. Richter at the California Institute of Technology. The magnitude is determined by readings of the seismic waves resulting from the earthquake's vibrations. For example, microearthquakes not generally felt by humans register about 2.0 or less on the Richter scale. With every whole point the magnitude rises, the strength of the waves increases tenfold. A temblor with a magnitude of 8.0 or more is considered a "great earthquake." To give you an idea how these numbers can add up, think of it in terms of the energy released by explosives: a magnitude 1 seismic wave releases as much energy as blowing up 6 ounces of TNT. A magnitude 8 earthquake releases as much energy as detonating 6 million tons of TNT 2

Richter Scale Richter Scale The formula for the Richter scale given in the Sullivan book measures the size of an earthquake in terms of the reading on a seismograph. The equivalent formula gives the same measurement in terms of the actual energy E in joules released by the earthquake. As can be seen from the following example, this formulation allows us to compare the actual strength of two earthquakes. Magnitude= Magnitude Earthquake Effects Estimated NumberEach Year 2.5 or less Usually not felt, but can be recorded by seismograph. 2.5 to 5.4 Often felt, but only causes minor damage. 5.5 to 6.0 Slight damage to buildings and other structures. 6.1 to 6.9 May cause a lot of damage in very populated areas. 7.0 to 7.9 Major earthquake. Serious damage. 8.0 or greater Great earthquake. Can totally destroy communities near the epicenter. 900,000 30,000 500 100 20 One every 5 to 10 years 3

Instruction Richter Scale Example: How many times stronger in terms of energy is a magnitude 6.8 earthquake than one which measures 6.0? 4

Question Richter Scale 1. How many times stronger is a magnitude 5.1 earthquake than one which measures 4.9? 5

Instruction Decibel Scale Decibel Scale The decibel scale measures the loudness of sound according to the formula Loudness= where x is the actual intensity of the sound measured in watts per square meter, and I0 = 10 12 watts per square meter the least intense sound that a human ear can detect. Similar to the previous example, we must use the formula in order to compare the intensity of two sounds. 6

Instruction Decibel Scale Example: How many times louder is a 108 decibel sound than a 100 decibel sound? 7

Question Decibel Scale 2. How many times louder is a 97 decibel sound than a 93 decibel sound? 8

Instruction ph Scale The ph scale is logarithmic and as a result, each whole ph value below 7 is ten times more acidic than the next higher value. For example, ph 4 is ten times more acidic than ph 5 and 100 times (10 times 10) more acidic than ph 6. The same holds true for ph values above 7, each of which is ten times more alkaline (another way to say basic) than the next lower whole value. For example, ph 10 is ten times more alkaline than ph 9 and 100 times (10 times 10) more alkaline than ph 8. ph Chart 9

Instruction ph Scale The formula for calculating ph is given by: ph= Where H + is the concentration of Hydrogen Ions in a solution. 10

Instruction ph Scale Example: How many times more acidic is a solution with ph=2.4 to a solution with a ph=4.1 11

Question Practice Questions 1) An earthquake in Japan measured 8.9 on the Richter Scale, and another in Italy was measured at 6.5. To the nearest whole number how many times more intense was the earthquake in Japan compared to the one in Italy? 12

Question Practice Questions 2) An earthquake hit Peru with measurement of 7.7 on the Richter Scale. The next day an aftershock occurred with 1/3 the intensity of the first earthquake. What was the Richter measurement of the aftershock? 13

Question Practice Questions 3) How many times more intense is a referee s whistle (125 db) compared to a Train whistle at 200m (90 db)? 14

Question Practice Questions 4) How many times louder is a clarinet (95 db) compared to a flute (89 db)? 15