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How Loud is Too Loud Activity

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How Loud is Too Loud Activity

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  1. The decibel (dB) is the unit to measure the intensity of a sound. It is a logarithmic unit used to express the ratio between two values of a physical quantity. The smallest audible sound (near total silence) is 0 dB. A sound 10 times more powerful is 10 dB. A sound 100 times more powerful (102) is 20 dB.In other words, when you increase sound (in terms of decibels) it is an exponential increase. How Loud is Too Loud Activity

  2. Audible wavelengths vary from animal to animal

  3. Properties of Logarithms

  4. What is a Logarithm? • A quantity representing the power to which a fixed number (the base) must be raised to produce a given number What is it used for? • Multiplying large numbers without the use of a calculator • Remember calculators were not readily available to the masses until about 50 years ago. We’ve come a LONG way since then in technology.

  5. Origin Greek Logos Reckoning, Ratio Arithmos number Modern Latin logarithmus Logarithm (log) Early 17th century Greek

  6. Why do we need Logarithms? • Calculators have advanced enough that even the most basic of calculators can easily compute logarithms for us, however, it’s important that we still understand the use of logarithms. • The exponential function y=axis one of the most important functions in mathematics, physics, and engineering. Radioactive decay, bacterial growth, population growth, continuous interest, etc. are all exponential examples we use everyday. • How do you solve for x if it is in the exponent? (y=ax) • We need logarithms to help us solve. y = ax is equivalent to loga(y) = x

  7. Examples Write the following in logarithmic/exponential form:

  8. Examples Evaluate the expression

  9. Different Bases:(We will practice logarithms using a variety of different bases.)Below you will find a list of the most common forms. • Base 10 is used by chemists in their measurements of pH, the acidity of a liquid. We often call this the common base. • Base 2 is used in information theory and computers (used in transmitting information and measuring the errors made and how to correct those errors). • Base e, where e=2.718281828..., is used in calculus and is probably the most important base.

  10. Let’s Discover the Properties of Logarithms…

  11. Here’s what you should have come up with…

  12. Here’s what you should have come up with… OR

  13. Here’s a few others for your notes…

  14. Let’s consider • Take the log of both sides • Use the multiplication law of logs to separate the right side of the equation into two separate logarithms • Use the exponent law of logs to simplify further, turning into 2 times log(a)

  15. The reverse is also trueConsider • Start with the exponent law of logarithms • Use the division/subtraction law of logarithms • Simplify • Note: We DID NOT DIVIDE BY LOG! This is not a defined mathematical principle. • We concluded that both sides of the equation had log10 therefore their values are equivalent.

  16. Let’s look at some real applications...

  17. Decibels

  18. A proposed city ordinance will make it illegal to create sound in a residential area that exceeds 72 decibels during the day and 55 decibels during the night. How many times as intense is the noise level allowed during the day than at night (Hint: is the equation for loudness, L, in decibels, when R is the relative intensity of the sound) times greater

  19. Earthquakes

  20. The magnitude of an earthquake is measured on a logarithmic scale called the Richter scale. The magnitude M is given by , where x represents the amplitude of the seismic wave causing ground motion. • How many times as great is the amplitude caused by an earthquake with a Richter scale rating of 7 as an aftershock with a Richter scale rating of 4? • How many times as great was the motion caused by the 1906 San Francisco earthquake that measured 8.3 on the Richter scale as that caused by the 2001 Bhuj, India, earthquake that measured 6.9? times greater times greater

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