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=(1)/(4) \sqrt{(\pi I)/(P) }`

B:
`r=(1)/(4) \sqrt{(P)/(\pi I) }`

C:
`r=(1)/(2) \sqrt{(\pi I)/(P) }`

D:
`r=(1)/(2) \sqrt{(P)/(\pi I) }`

Answer 1

Plato answer is d

Answer 2

D: r=1/2 sqrt(P/πI)

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