Question

The sound intensity at a distance of 16 m from a noisy generator is measured to be 0.25 W/m2. What is the sound intensity at a distance of 28 m from the generator?

Answer 1

Answer:

0.1111 W/m²

Explanation:

If all other parameters are constant, sound intensity is inversely proportional to the square of the distance of the sound. That is,

I ∝ (1/r²)

I = k/r²

Since k can be the constant of proportionality. k = Ir²

We can write this relation as

I₁ × r₁² = I₂ × r₂²

I₁ = 0.25 W/m²

r₁ = 16 m

I₂ = ?

r₂ = 24 m

0.25 × 16² = I₂ × 24²

I₂ = (0.25 × 16²)/24²

I₂ = 0.1111 W/m²

Answer 2

The sound intensity at a distance of 28 m from the generator will be "0.1111 W/m²".

Distance and Sound intensity

According to the question,

Distance, r₁ = 16 m

                r₂ = 28 m

Sound intensity, I₁ = 0.25 W/m²

We know the relation,

→ I ∝ ($\frac{1}{r^2}$)

or,

  I ∝ $\frac{k}{r^2}$

Now,

→ I₁ × r₁² = I₂ × r₂²

By substituting the values,

0.25 × (16)² = I₂ × (24)²

                I₂ = $\frac{0.25\timers (16)^2}{(24)^2}$

                   = 0.1111 W/m²

Thus the above answer is correct.

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