A sound level of 96 dB is how many times as intense as one of 90 dB?

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A sound level of 96 dB is how many times as intense as one of 90 dB?

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Kiệt Gia 3 years 2021-08-29T14:32:17+00:00 1 Answers 28 views 0

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  1. trungdung22
    0
    2021-08-29T14:33:19+00:00
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    Answer:

    A sound level of 96 dB is 4 times as intense as one of 90 dB

    Explanation:

    The formula of the intensity level of sound in decibels is given as follows:

    Intensity Level = 10 log₁₀(I/I₀)

    where,

    I = Intensity of Sound

    I₀ = Reference Intensity Level = 10⁻¹² W/m²

    Therefore, for 96 dB sound level:

    96 = 10 log₁₀(I₁/10⁻¹²)

    log₁₀(I₁/10⁻¹²) = 96/10

    I₁/10⁻¹² = 10^9.6

    I₁ = (10⁻¹²)(4 x 10⁹)

    I₁ = 0.004 W/m²

    For 90 dB sound level:

    90 = 10 log₁₀(I₂/10⁻¹²)

    log₁₀(I₂/10⁻¹²) = 90/10

    I₂/10⁻¹² = 10^9

    I₂ = (10⁻¹²)(10⁹)

    I₂ = 0.001 W/m²

    Therefore,

    I₁/I₂ = 0.004/0.001

    I₁ = 4 I₂

    Hence, the sound level of 96 dB is 4 times as intense as one of 90 dB.

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