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9 March, 14:44

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) ?

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  1. 9 March, 15:12
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    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
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