A person standing 1.00 m from a portable speaker hears its sound at an intensity of...

A person standing 1.00 m from a portable speaker hears its sound at an intensity of 7.50 × 10−3 W/m2 .

(a) Find the corresponding decibel level.

(b) Find the sound intensity at a distance of 35.0 m, assuming the sound propagates as a spherical wave.

Solutions

Expert Solution

Initial distance of the person from the portable speaker = R₁ = 1 m

Sound intensity at this distance = I₁ = 7.5 x 10^-3 W/m²

Sound intensity level at this distance = ₁

₁ = 98.75 dB

New distance from the portable speaker = R₂ = 35 m

Sound intensity at this new distance = I₂

Sound propagates as a spherical wave therefore the power is equally distributed in a spherical manner.

I₁(4R₁²) = I₂(4R₂²)

I₁R₁² = I₂R₂²

(7.5x10^-3)(1)² = I₂(35)²

I₂ = 6.122 x 10^-6 W/m²

Sound intensity level at this new distance = ₂

₂ = 67.87 dB

a) Decibel level at a distance of 1 m = 98.75 dB

b) Sound intensity at a distance of 35 m = 6.122 x 10^-6 W/m²

c) Decibel level at a distance of 35 m = 67.87 dB

genius_generous answered 1 year ago

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