The decibel level of a sound is given by the equation D=10log 10 (i/i 0), where "i" is the sound's intensity and "i 0" corresponds to the intensity of the weakest sound that can be detected by the human ear. Approximately how many times greater than "i 0" must the intensity "i" of a sound be to reach 140 decibels?

Question

The decibel level of a sound is given by the equation D=10log 10 (i/i 0), where "i" is the sound's intensity and "i 0" corresponds to the intensity of the weakest sound that can be detected by the human ear. Approximately how many times greater than "i 0" must the intensity "i" of a sound be to reach 140 decibels?
A. 14 times greater
B. 1.14612 times greater
C. 10^14 times greater
D. 22026 times greater
E. 2.63906 times greater

oobleck · Accepted Answer

10log 10 (i/i0) = 140 log (i/i0) = 14 i/i0 = 10^14