SOLUTION: In the examples, my book roughly says "for sounds with intensity "I" (in watts per square meter), the loudness L(I) of the sound (in decibels) is given by the function " L(I) = 10l

Algebra ->  Logarithm Solvers, Trainers and Word Problems -> SOLUTION: In the examples, my book roughly says "for sounds with intensity "I" (in watts per square meter), the loudness L(I) of the sound (in decibels) is given by the function " L(I) = 10l      Log On


   

Question 948537: In the examples, my book roughly says "for sounds with intensity "I" (in watts per square meter), the loudness L(I) of the sound (in decibels) is given by the function " L(I) = 10log( I / Isub0 " where Isub0 is the intensity of a barely audible sound (about 10^-12 watts per square meter).
However, the problem in the homework asks "The intensity of the sound of a trumpet is 10^3 watts per square meter. Find the decibel level of a trumpet."
I tried guessing what to do with Isub0 (which was not written like that but I dont really know how to type that here) and i did not have any idea what to do. I hope you can help!
Answer by MathLover1(20850) About Me  (Show Source):
You can put this solution on YOUR website!

given:
The intensity of the sound of a trumpet is I=10%5E3 watts per square meter.
The intensity of a barely audible sound I%5B0%5D=+10%5E-12+ watts per square meter.
Find the decibel level of a trumpet.

L%28I%29+=+10log%28+I+%2F+I%5B0%5D%29...........plug in given values
L%28I%29+=+10log%2810%5E3%2F10%5E%28-12%29%29
L%28I%29+=+10log%2810%5E3%2F%281%2F10%5E12%29%29
L%28I%29+=+10log%2810%5E3%2A10%5E12%29

L%28I%29+=+10log%2810%5E%283%2B12%29%29

L%28I%29+=+10log%2810%5E15%29 ......log%2810%5E15%29=15
L%28I%29+=+10%2A15
L%28I%29+=+150 which is the decibel level of a trumpet