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 1 year 2021-08-22T05:38:54+00:00 1 Answers 33 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

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

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

    Using formula of sound intensity

    [tex]dB=10\log(\dfrac{I_{a}}{I_{o}})[/tex]

    Put the value into the formula

    [tex]20=10\log(\dfrac{I_{a}}{10^{-12}})[/tex]

    [tex]10^{2}=\dfrac{I_{a}}{10^{-12}}[/tex]

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

    If the conversation a sound level of 70.0 dB instead

    We need to calculate the sound intensity

    Using formula of sound intensity

    [tex]dB=10\log(\dfrac{I_{b}}{I_{o}})[/tex]

    Put the value into the formula

    [tex]70=10\log(\dfrac{I_{a}}{10^{-12}})[/tex]

    [tex]10^{7}=\dfrac{I_{b}}{10^{-12}}[/tex]

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

    We know that,

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

    We need to calculate the distance

    Using formula of intensity

    [tex]\dfrac{I_{a}}{I_{b}}=\dfrac{R_{b}^2}{R_{a}^2}[/tex]

    Put the value into the formula

    [tex]\dfrac{10^{-10}}{10^{-5}}=\dfrac{R_{b}^2}{20^2}[/tex]

    [tex]R_{b}^2=20^2\times\dfrac{10^{-10}}{10^{-5}}[/tex]

    [tex]R_{b}=\sqrt{20^2\times\dfrac{10^{-10}}{10^{-5}}}[/tex]

    [tex]R_{b}=0.063\ m[/tex]

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

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