You are standing 7.0 meters from a sound source that radiates equally in all directions, but it is too loud for you. How far away from the source should you stand to experience one third the intensity that you did at 7.0 meters? answer in meters

You have to clarify this: Are you speaking of intensity as in power, or db?

Folks use the term intensity in many ways.

yes i am talking intensity. sorry.

To determine the distance from the sound source where you would experience one third the intensity of the original sound, we can use the inverse square law for sound intensity.

The inverse square law states that the intensity of sound decreases inversely with the square of the distance from the source. Mathematically, it can be expressed as:

I₁ / I₂ = (r₂ / r₁)²

Where:
I₁ is the initial sound intensity (unknown)
I₂ is the desired sound intensity (1/3 of the initial intensity)
r₁ is the initial distance from the sound source (7.0 meters)
r₂ is the unknown distance we need to find

Rearranging the equation to solve for r₂, we have:

(r₂ / r₁)² = I₁ / I₂

Taking the square root of both sides:

r₂ / r₁ = √(I₁ / I₂)

Now we can substitute the values and solve for r₂:

r₂ / 7.0 = √(I₁ / (1/3))

Simplifying further:

r₂ / 7.0 = √(3I₁)

Multiplying both sides by 7.0:

r₂ = 7.0 * √(3I₁)

Since the initial sound intensity (I₁) is unknown, we need additional information to find the answer.