SOLUTION: A law of physics states that the intensity of sound is inversely proportional to the square of the distance d of the source I: k/d^2 a. Use this model and the equation B=10log(I

Question 815145: A law of physics states that the intensity of sound is inversely proportional to the square of the distance d of the source I: k/d^2
a. Use this model and the equation B=10log(I/I0) to show that the decibel levels B1 and B2 at distances d1 and d2 from a sound source are related by the equation B1= B2-20log(d1/d2)
I'm a little confused. Help?

Answer by jsmallt9(3758) (Show Source): You can put this solution on YOUR website!
Since then
and

We want and in the same equation. So we will combine the two above by adding or subtracting them. I can see ahead that subtraction will make things a little easier so we will subtract the second equation from the first one:

Adding to each side:

As you can, the desired equation is starting to appear. We just need to manipulate the right side so that

the I's are gone
The d's are there
And it looks like the desired equation. The I's and d's are related by the equation: . So and . Substituting for and we get:

Most of the I's are gone and we have the d's. All that is left is to eliminate the 's and the k's and make the equation look like the one we want. We do want only one log so I combine the two we have next. Factoring out 10:

Now we can use the property to combine the logs:

Rewriting the division of fractions as a multiplication by the reciprocal:

...and the 's and the k's cancel out!

which simplifies to:

We're getting very close. Rewriting the fraction:

Using the property:

Multiplying the 10 and 2:

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