# hw4_soln - 2.011 HW 4 Solution Set Problem 1(10 points a(2...

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2.011 3/22/06 HW# 4 Solution Set Problem 1: (10 points) a. (2 points)The decibel ( dB ) is a measure of the ratio between two quantities, and is used in a wide variety of measurements in acoustics, physics and electronics. While originally only used for power and intensity ratios, it has come to be used more generally in engineering. The decibel is widely used as a measure of the loudness of sound. It is a "dimensionless unit" like percent. Decibels are useful because they allow even very large or small ratios to be represented with a conveniently small number. This is achieved by using a I dB = 10log 10 ( I I 0 ) P dB = 10log10( P P 0 ) logarithm. Intensity is I and pressure is denoted by P. b. (3 points) i. Jet engine – 130 dB @ 30 m ii. Car – motorcycle accelerating @ 5m = 110 dB iii. Whale – Blue Whale humming at 1m = 180 dB iv. Underwater Seismic Activity - seafloor volcanic eruption = 255 unerwater dB @ 1m. v. Rock concert – average is about 100 dB vi. Ships propeller – Supertanker = ~127 dB in air and 190 dB in water vii. Dolphin - 208 dB in water @ 6 m. c. (3 points) i. 10log 10 (A/B) = 10*(log 10 (A) - log 10 (B)) = log 10 (A 10 ) - log 10 (B 10 ) ii. 10log 10 (A+B) = log 10 ((A+B) 10 ) iii. 10log 10 (A B ) = B*10* log 10 (A) d. (2 points) i. 10log

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hw4_soln - 2.011 HW 4 Solution Set Problem 1(10 points a(2...

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