Mrs. Hayden Name______________________________ Date___________ 10 – 4 Applications of Common Logs Relative Intensity of Sound The intensity of the faintest sound audible to the human ear is called the threshold of hearing. It is 10-12 watts per meters squared. Sound intensities, I, are compared with the threshold of hearing, I o, producing a ratio. The relative intensity, R, of a sound in decibels (dB) is given by the function I I = sound intensity, I 0 the threshold R 10 log , where I0 of hearing I R 10 log 0 10 log 1 0 threshold of hearing = 0 decibels I0 1. The intensity of a whisper is about 300 times as loud as the threshold of hearing, I 0 . Find the relative intensity, R, in decibels. 2. The relative intensity of a vacuum cleaner is about 70 decibels. Compare this to the threshold of hearing. 3. The relative intensity of a loud siren is about 1013 times as loud as the threshold of hearing, I 0 . Find the relative intensity, R, of the loud siren, in decibels. 4. The sound of a leaf blower is about 1010.5 times the intensity of the threshold of hearing, I 0 . Find the relative intensity, R, of this leaf blower in decibels. Mrs. Hayden 5. Suppose that the relative intensity, R, of a rock band is about 115 decibels. Compare the intensity of this band with that of the threshold of hearing, I 0 . 6. A small jet engine produces a sound whose intensity is one billion times as loud as the threshold of hearing. What is the relative intensity of the engine’s sound in decibels? 7. Conversation is about 350,000 times the intensity of the threshold of hearing. Find the relative intensity, R, in decibels. pH level of a substance: In chemistry, the pH of a substance is defined as pH log H , where H is the hydrogen ion concentration in moles per liter. An acidic solution has a pH value in the range 0 < pH < 7. An alkaline solution has a pH value in the range 7 < pH < 14. 8. For hydrochloric acid, H is about 5 10 2 moles per liter. Find the pH for this strong acid to the nearest tenth. 9. For milk of magnesia, H is about 3.2 10 11 moles per liter. Find the pH of milk of magnesia to the nearest tenth. 10. Find the pH of orange juice: H 3.16 10 4 moles per liter. Mrs. Hayden Magnitude of earthquakes On the Richter scale, the magnitude, M, of an earthquake depends on the amount of energy, E, released by the earthquake as follows: log E = 11.8 + 1.5M The amount of energy E, measured in ergs, is based on the amount of ground motion recorded by a seismograph at a known distance from the epicenter of the quake. The logarithmic function for the Richter scale assigns very large numbers for the amount of energy, E, to numbers that range from 1 to 9. A rating of 2 on the Richter scale indicates the smallest tremor that can be detected. Destructive earthquakes are those rated greater than 6 on the Richter scale. -------------------------------------------------------------------------------------11. In 1976, an earthquake that released about 8 1019 ergs of energy occurred in San Salvador, El Salvador. Find the magnitude, M, of this earthquake to the nearest tenth. 12. One of the strongest earthquakes in recent history occurred in Mexico City in 1985. The amount of energy released by this earthquake was approximately 8.91 10 23 ergs. Find the magnitude, M, of this earthquake to the nearest tenth. 13. In 1989, an earthquake that measured 7.1 on the Richter scale occurred in San Francisco, CA. Find the amount of energy, E, released by this earthquake. 14. On May 10, 1997, a light earthquake with a magnitude of 4.7 struck the Calaveras Fault 10 miles east of San Jose, California. Find the amount of energy, E, released by this earthquake.