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

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SUMMARY

The problem involves calculating the distance of two identical car horns based on their sound intensity ratio of 6:1. Given that the nearer car is 8 meters away, the solution requires applying the formula for intensity, I ∝ 1/r². By setting up the equation 6/1 = R²/8², the distance of the more distant car can be determined to be approximately 19.6 meters. This conclusion is reached by manipulating the intensity ratio and solving for R.

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  • Understanding of sound intensity and its relationship with distance.
  • Familiarity with the formula for intensity: Intensity = P / (4πR²).
  • Knowledge of ratios and how to manipulate them mathematically.
  • Basic algebra skills for solving equations.
NEXT STEPS
  • Study the principles of sound intensity and wave propagation.
  • Learn about the mathematical derivation of the intensity formula.
  • Explore practical applications of sound intensity in real-world scenarios.
  • Investigate the effects of distance on sound perception in different environments.
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Students studying physics, particularly those focusing on acoustics, as well as educators seeking to enhance their understanding of sound intensity concepts.

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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
 
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I ∝ 1/r²

So the ratio of I1/I2 = R2² /R1²

That suggests then that

6/1 = R²/8² then isn't it?
 

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