You are trying to overhear a juicy conversation, but from your distance of 20.0 m, it sounds like only an average whisper of 20.0 dB. So you

Question

You are trying to overhear a juicy conversation, but from your distance of 20.0 m, it sounds like only an average whisper of 20.0 dB. So you decide to move closer to give the conversation a sound level of 70.0 dB instead. How close should you come?

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RI SƠ 5 months 2021-08-22T05:38:54+00:00 1 Answers 6 views 0

Answers ( )

    0
    2021-08-22T05:40:27+00:00

    Given that,

    Distance = 20.0 m

    Average whisper = 20.0 dB

    Sound level = 70.0 dB

    We know that,

    The minimum intensity is

    I_{o}=10^{-12}\ W/m^2

    We need to calculate the sound intensity in the distance of 20 m

    Using formula of sound intensity

    dB=10\log(\dfrac{I_{a}}{I_{o}})

    Put the value into the formula

    20=10\log(\dfrac{I_{a}}{10^{-12}})

    10^{2}=\dfrac{I_{a}}{10^{-12}}

    I_{a}=10^{-10}\ W/m^2

    If the conversation a sound level of 70.0 dB instead

    We need to calculate the sound intensity

    Using formula of sound intensity

    dB=10\log(\dfrac{I_{b}}{I_{o}})

    Put the value into the formula

    70=10\log(\dfrac{I_{a}}{10^{-12}})

    10^{7}=\dfrac{I_{b}}{10^{-12}}

    I_{b}=10^{-5}\ W/m^2

    We know that,

    The intensity is inversely proportional with the square of the distance.

    We need to calculate the distance

    Using formula of intensity

    \dfrac{I_{a}}{I_{b}}=\dfrac{R_{b}^2}{R_{a}^2}

    Put the value into the formula

    \dfrac{10^{-10}}{10^{-5}}=\dfrac{R_{b}^2}{20^2}

    R_{b}^2=20^2\times\dfrac{10^{-10}}{10^{-5}}

    R_{b}=\sqrt{20^2\times\dfrac{10^{-10}}{10^{-5}}}

    R_{b}=0.063\ m

    Hence, The distance from the conversation should be 0.063 m.

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