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## 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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Physics
1 year
2021-08-22T05:38:54+00:00
2021-08-22T05:38:54+00:00 1 Answers
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## Answers ( )

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 mUsing 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 intensityUsing 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 distanceUsing 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.