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LSP 121 -- Homework 3b

Logarithmic Units

Show your work for each problem. You can submit an Excel file if you wish.

Part B: Logarithmic Units

  1. The strength of an earthquake can be measured either by its intensity I or by its Richter number R. The values I and R are related by R = log(I) and I = 10R.

    1. Given an earthquake with Richter number 8.3, what is its intensity?

    2. Given an earthquake with intensity 23,345,000, what is its Richter number?

    3. 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 earthquake be than the first?

    4. If one earthquake had an intensity of 8,000,000 and another had an intensity of 80,000,000 how, would their Richter numbers compare?

  2. The loudness of a sound can be measured by its intensity I or in decibels D. A sound of zero decibels (the threshold of hearing) is the quietest sound that can be heard by the human ear; on the other extreme, a sound of 160 decibels will cause instant rupture of the eardrum. The values I and D are related by D = 10 * log(I) and I = 10D/10.

    1. If a sound measures 49 decibels, what is its intensity?

    2. If a sound has intensity 47,983, what is its measurement in decibels.

    3. If one sound has an intensity of 300,000 and another sound has an intensity of 30,000,000, how many decibels louder is the second sound than the first?

    4. A sound of 70 decibels is how many times louder than the threshold of hearing?