jim halves the distance between himself and a sound source. What is the change of decibels of the sound he hears?

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jim halves the distance between himself and a sound source. What is the change of decibels of the sound he hears?

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Orla Orla 2 weeks 2021-07-19T20:44:24+00:00 1 Answers 0 views 0

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    2021-07-19T20:45:41+00:00

    Answer:

    6.02dB

    Explanation:

    The sound level intensity can be calculated by using the formula:

    I(dB)=10log_{10}(\frac{I}{I_o})

    where Io is the threshold of human hearing, and  I is the intensity of the sound in at a certain distance. I is given by

    I=\frac{P}{4\pi r^2}

    where P is the power of the source and r is the distance to the source. By replacing I in the expression for I(dB) we obtain

    I(dB)=10log(\frac{P}{4\pi r^2I_o})=10log(\frac{P}{\pi r^2I_o})-10log(4)

    when jim halves the distance we have r’=1/2r:

    I'(dB)=10log(\frac{P}{4\pi (\frac{1}{2}r)^2I_o})=10log(\frac{P}{\pi r^2I_o})

    Hence, the change o decibels is:

    I'-I=10log(4)=6.02dB

    hope this helps!!

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