SOLUTION: Remember the definition of a decibel: dB=10log(I×10^12) where dB is the magnitude on the decibel scale and I is the intensity of the sound wave. If a quiet whisper is 30 dB

Algebra ->  Logarithm Solvers, Trainers and Word Problems -> SOLUTION: Remember the definition of a decibel: dB=10log(I×10^12) where dB is the magnitude on the decibel scale and I is the intensity of the sound wave. If a quiet whisper is 30 dB       Log On


   

Question 962834: Remember the definition of a decibel:
dB=10log(I×10^12)
where dB is the magnitude on the decibel scale and I is the intensity of the sound wave. If a quiet whisper is 30 dB and the sound of a train whistle is 90 dB, how many times more intense is the sound of a train whistle than a whisper?
Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
whisper:
+30+=+10%2Alog%28+I%2A10%5E12+%29+
+log%28+I%2A10%5E12+%29+=+3+
+10%5E3+=+10%5E12%2AI+
+I+=+10%5E3%2A10%5E%28%28-12%29%29+
+I+=+10%5E-9+
------------------
train whistle:
+90+=+10%2Alog%28+I%2A10%5E12+%29+
+log%28+I%2A10%5E12+%29+=+9+
+10%5E9+=+10%5E12%2AI+
+I+=+10%5E9%2A10%5E%28%28-12%29%29+
+I+=+10%5E-3+
-------------------
+10%5E-3+=+k%2A10%5E-9+
+k+=+10%5E-3+%2F+10%5E-9+
+k+=+10%5E-3%2A10%5E9+
+k+=+10%5E6+
---------------------
the train whistle is 10^6 or
one million times more
intense than the whisper