Sound 1 has an intensity of 38 W/m2. Sound 2 has an intensity level that is 2.5 dB greater than the intensity level of sound 1. What is the

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Sound 1 has an intensity of 38 W/m2. Sound 2 has an intensity level that is 2.5 dB greater than the intensity level of sound 1. What is the intensity of sound 2?

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Thanh Thu 4 years 2021-08-27T21:33:09+00:00 1 Answers 51 views 0

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  1. Tryphena
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    2021-08-27T21:35:01+00:00
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    Answer:

    The intensity of sound 2 is 67.6 W/m²

    Explanation:

    First we convert the intensity of sound 1 to the intensity level in db:

    For this we use the formula:

    L₁ = 10 log₁₀[I₁/I₀]

    where,

    L₁ = intensity level of sound 1

    I₁ = Intensity of sound 1 = 38 W/m²

    I₀ = Minimum Audible Intensity = 10⁻¹² W/m²

    Therefore:

    L₁ = 10 log₁₀ [38/10⁻¹²]

    L₁ = 135.8 dB

    Since, the intensity level of sound 2 is 2.5 dB greater than intensity level of sound 1. Therefore,

    L₂ = 135.8 dB + 2.5 dB

    L₂ = 138.3 dB

    Now, we calculate intensity of sound by the same formula:

    L₂ = 10 log₁₀[I₂/I₀]

    10^(L₂/10) = [I₂/I₀]

    (I₀)[10^(L₂/10)] = I₂

    where,

    L₂ = intensity level of sound 2 = 138.3 dB

    I₂ = Intensity of sound 2 = ?

    I₀ = Minimum Audible Intensity = 10⁻¹² W/m²

    Therefore:

    I₂ = (10⁻¹²)(10^13.83)

    I₂ = 10^1.83

    I₂ = 67.6 W/m²

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