What is the decibel level of the radio with intensity 10−7 watts per square inch? Use a logarithmic model to solve.

Question

What is the decibel level of the radio with intensity 10−7 watts per square inch? Use a logarithmic model to solve.

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Yến Oanh 3 months 2021-09-02T04:34:03+00:00 1 Answers 0 views 0

Answers ( )

  1. Answer:

    D = 50

    Step-by-step explanation:

    Given

    I = 10^{-7}W/m^2 — Intensity

    Required

    Determine the decibel level (D)

    This is calculated as:

    D = 10 * log(\frac{I}{I_n})

    Where:

    I_n = The threshold intensity

    I_n =1 * 10^{-12}W/m^2

    So, we have:

    D = 10 * log(\frac{I}{I_n})

    This gives:

    D = 10 * log(\frac{10^{-7}W/m^2}{1 * 10^{-12}W/m^2})

    D = 10 * log(\frac{10^{-7}}{10^{-12}})

    Apply law of indices

    D = 10 * log(10^{-7--12})

    D = 10 * log(10^{5})

    Apply law of logarithm

    loga^b = b\ log(a)

    So, we have:

    D = 10 * 5 * log(10)

    log(10)  =1

    So:

    D = 10 * 5 *1

    D = 50

    Hence, the decibel level is 50

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