Residents of hawaii are warned of the approach of a tsunami by sirens mounted on the tops of towers. suppose a siren produces a sound that has an intensity level of 120 db at a distance of 2 m. treating the siren as a point source of sound, and ignoring reflections and absorption,

a. what is the sound intensity level heard by an observer at a distance of 12 m

b. what is the sound intensity level heard by an observer at a distance of 21 m?

c. how far away can the siren be heard? (i = threshold of hearing)

a)  I₂ = 2.78 10⁻² W / m² , b)  I₃ = 9 10⁻² W/m² , c) R₄ = 2 10⁶ m

Explanation:

The intensity of a wave is defined as the emission power per unit area

         I = P / A

The unit of decibels is defined by

        β = 10 log (I / Io)

With Io the hearing threshold 10⁻¹² W / m²

a) the intensity at r = 12m

Let's use the first equation

        P = IA

        I₁ A₁ = I₂ A₂

Let's look for intensity (I₁)

       β / 10 = log I₁ / I₀

       I / I₀ =

       I = I₀

       I = 1 10⁻¹²

       I = 1 W / m²

The area of a spherical surface is

       A = 4π R²

       I₁ r₁² = I₂ r₂²

       I₂ = I₁ R₁² / r₂²

       I₂ = I₁ 2²/12²

       I₂ = 1 2.78 10⁻²

       I₂ = 2.78 10⁻² W / m²

b) r = 21 m

       I₃ = I₁ r₁² / r₃²

       I₃ = 1 2²/21²

       I₃ = 9 10⁻² W/m²

c) in this case I₄ = I₀

       I₁ r₁² = I₄ r₄²

       R₄² = I₁ / I₄ r₁²

       R₄² = 1 / 10⁻¹²  2²

       R₄² = 4 10¹²

       R₄ = 2 10⁶ m

and 1and 1