Question

A microphone receiving a pure sound tone feeds an oscilloscope, producing a wave on its screen. If the sound intensity is originally 2.00 x 10-5 W/m2 , but is turned up until the amplitude increases by 30.0%, what is the new intensity (W/m2)?

Answer 1

Answer:

The new intensity = 3.38 × 10⁻⁵ W/m²

Explanation:  

Intensity of sound wave:

The intensity of sound  is the rate of flow of flow of energy, per unit area, perpendicular to the direction of the sound wave.

Intensity (I) ∝ A²

where I = intensity, A = Amplitude.

∴ I₁/I₂ = A₁²/A²₂............................... equation 1

From the question, the amplitude increase by 30% of the initial

∴ A₂ = A₁ + 0.3A₁ = 1.3A₁, I₁ = 2.00×10⁻⁵ W/m²

∴ (2.00×10⁻⁵)/I₂ = A₁²/(1.3A₁)²

(2.00×10⁻⁵)/I₂ = 1/1.3²

 making I₂ the subject of the equation

I₂ = (2.00 × 10⁻⁵)×1.3² = 3.38 × 10⁻⁵ W/m₂

The new intensity = 3.38 × 10⁻⁵ W/m²