HW 11: Problem 18 Previous Problem List Next (1 point) The decibel rating D is r

Question

HW 11: Problem 18 Previous Problem List Next (1 point) The decibel rating D is related to the sound intensity I by the formula D = 10 10 16for the noise level in decibels (a) Let D and d the difference between the two ratings, D-d, in terms of the two intensities 1 and i. D-d= represent the decibel ratings of sounds of intensity / and i, respectively. Using properties of logarithms, find a simplified formula for El help (oganithms) Enter log10 or logten for the base 10 logarithm.) (b) If a sound's intensity triples, how many decibels louder does the sound become? l decibels help (numbers) Note: You can earn partial credit on this problem Preview My Answers Submit Answers

Explanation / Answer

D = 10 log 10 ( I / 10^-16 )

d = 10 log 10 ( i / 10^-16 )

D - d = 10 log 10 ( I / 10^-16 ) - 10 log 10 ( i / 10^-16 )

= 10 [ log 10 ( I / 10^-16 ) - log 10 ( i / 10^-16 ) ]

= 10 [ log 10  ( I / 10^-16 / i / 10^-16 ) ]

D - d = 10 [ log 10 ( I / i ) ]

b) if sound intensty triples

D = 10 log 10 ( 3I / I )

= 4.77 decibels

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