Please help me out with the length on this sound intensities problem

[jvirus872000]

Homework Statement

When sounded separately, two identical car horns produce sound intensities at your ear in the ratio 6:1. If the nearer car is 8m from you, how far from you is the more distant car? Assume uniform spherical wavefronts.

Homework Equations

Intensity=P/4x(3.14)"pi"x R^2
ratio fartest car=(ratio nearest car+ratio that i am)^1/2<<"squareroot"

The Attempt at a Solution

All I did was the surface area for the sphere, which was
4x3.14x8^2= 1607.7
Then i do not know what else to do because i need to find the length, I know the answer should be 19.6

 

[LowlyPion]

Welcome to PF.

I ∝ 1/r²

So the ratio of I₁/I₂ = R₂² /R₁²

That suggests then that

6/1 = R²/8² then isn't it?

 

[thomate1]

m

I would first commend you for attempting to solve this problem on your own. It shows that you are thinking critically and trying to apply the equations you have learned. However, I can provide some guidance on how to approach this problem.

First, let's define some terms to make things clear. The sound intensity is the power of the sound wave per unit area. In this case, we can use the equation you provided: Intensity = Power / (4 x pi x R^2), where R is the distance from the sound source.

Next, let's set up the problem. We have two identical car horns, and we are given the ratio of their sound intensities at your ear (6:1). This means that the intensity of the nearer car is 6 times greater than the intensity of the more distant car. We also know that the nearer car is 8m from you.

Now, let's use the equation for intensity to solve for the distance of the more distant car. We can set up the following equation:

Intensity of nearer car = Power / (4 x pi x 8^2) = 6 x Intensity of more distant car

We can rearrange this equation to solve for the intensity of the more distant car:

Intensity of more distant car = Power / (4 x pi x 8^2) / 6

Next, we can use the given ratio (6:1) to find the power of the more distant car. Since the ratio is 6:1, we can say that the power of the more distant car is 1/6 of the power of the nearer car.

Finally, we can substitute this value for power into the equation for intensity and solve for R, the distance of the more distant car. This gives us:

Intensity of more distant car = (1/6 x Power) / (4 x pi x R^2)

Since we know the intensity of the more distant car and the power of the more distant car (1/6 of the power of the nearer car), we can solve for R:

(1/6 x Power) / (4 x pi x R^2) = Power / (4 x pi x 8^2) / 6

Solving for R gives us R = 19.6m, which is the distance of the more distant car.

In summary, to solve this problem, we used the equation for intensity and