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The sound intensity a distance d1 = 15.0 m from a chain saw is 0.260 W/m2. What is the sound intensity a distance d2 = 27.0 m from the chain saw? (Enter your answer in W/m

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boffeemadrid

Answer:

0.08024 W/m²

Explanation:

P = Power

[tex]d_1[/tex] = Distance = 15 m

[tex]I_1[/tex] = Intensity at 15 m = 0.26 W/m²

[tex]d_2[/tex] = Distance = 27 m

[tex]I_1[/tex] = Intensity at 27 m

Sound intensity is given by

[tex]I=\frac{P}{4\pi d^2}[/tex]

[tex]\\\Rightarrow I\propto \frac{1}{d^2}[/tex]

So, we have the relation

[tex]\frac{I_1}{I_2}=\frac{d_2^2}{d_1^2}\\\Rightarrow I_2=\frac{d_1^2\times I_1}{d_2^2}\\\Rightarrow I_2=\frac{15^2\times 0.26}{27^2}\\\Rightarrow I_2=0.08024\ W/m^2[/tex]

The sound intensity at the given distance is 0.08024 W/m²

Eduard22sly

The sound intensity at a distance (d₂ = 27.0 m) from the chainsaw having a sound intensity of 0.260 W/m² at a distance (d₁ = 15 m) is 0.08 W/m²

Data obtained from the question

  • Distance 1 (d₁) = 15 m
  • Intensity 1 (I₁) = 0.260 W/m²
  • Distance 2 (d₂) = 27 m
  • Intensity 2 (I₂) =?

How to determine the intensity

The sound intensity at the distance d₂ = 27 m can be obtained as follow:

I₁d₁² = I₂d₂²

0.26 × 15² = I₂ × 27²

0.26 × 225 = I₂ × 729

58.5 = I₂ × 729

Divide both side by 729

I₂ = 58.5 / 729

I₂ = 0.08 W/m²

Learn more about sound intensity:

https://brainly.com/question/26861471

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