Question

Sound waves can be ranked by their intensity, I, given in the formula below, where r is the distance from the source of a sound with a power output of P.
P=4πIr²

Solve the formula for the distance from the source, r.

A: $r=\frac{1}{4} \sqrt{\frac{\pi I}{P} }$

B: $r=\frac{1}{4} \sqrt{\frac{P}{\pi I} }$

C: $r=\frac{1}{2} \sqrt{\frac{\pi I}{P} }$

D: $r=\frac{1}{2} \sqrt{\frac{P}{\pi I} }$

Answer 1

Answer:

D: r=1/2 sqrt(P/πI)

Step-by-step explanation:

P=4πIr²

We want to solve the equation for r

First divide each side of the equation by 4πI

P/4πI =4πIr²/4πI

P/4πI =r²

Then we need to take the square root of each side.  Normally we would take the ± square root, but distance cannot be negative.

sqrt(P/4πI)  = sqrt(r²)

sqrt(P/4πI)  = r

Notice that there is a 4 in the denominator.  sqrt(4) = 2

sqrt(P/πI)* 1/sqrt(4)  = r

sqrt(P/πI)* 1/2  = r

1/2 sqrt(P/πI) = r